1986-11 Spring 1986

Green's Creek Dairy, LTD.:

SOUTHERN METHODIST UNIV Optimal Feed-MLx Solutions Using Linear Programming

Formulations

Daniel Marzoula Michael Ganz

GREEN'S CREEK DAIRY, LTD.

I OPTIMAL FEED-MIX SOLUTIONS

USING

ILINEAR PROGRAMMING FORUMLATIONS

DEPARTMENT OF OPERATIONS RESEARCH AND ENGINEERING MANAGEMENT

SCHOOL OF ENGINEERING AND APPLIED SCIENCE DALLAS, TEXAS 75275

I I I I I

GREEN'S CREEK DAIRY, LTD.

I OPTIMAL FEED-NIX SOLUTIONS

USING

LINEARLINEAR PROGRAMMING FORUMLATIONS

I I' I I I I I I I I I I

Date: May 10, 1986

For: Southern Dairy Ngnit.

By: Daniel Marzoula & Michael Ganz

To: Dr. Richard Barr OREM Department Southern Methodist University

ABSTRACT

big business. It doesn't matter what the

is, or the number of cows, or the number of

ming today is big business and management

dependent upon access to appropriate

considering decisions effecting the profit

business.

II

Dairy farming is

size of the farm

workers. All fa:

demands and is

information when

potential of the

IOperations research can be a big help to management when it

comes to solving the best solution for particular dairy I problems. The dairyman who uses facts for his decisions and

wisely utilizes all of his resources -- information, cattle, I and feed -- will be the one who reaps the greatest profits.

We chose to focus mainly on feed-mix programs for our

project. The following report will discuss in detail what

we believe is the best solution to solve the problems

dairymen face each day with maximizing the overall milk

production.

I

I I I I INTRODUCTION

A. Scope B. Purpose C. Plan of Development D. Intentions

REPORT

I

II

A. Feed-Mix B. Problem C. Protein D. Fat E. Calcium & Phosphorous F. Sodium I G. Water H. Drying off cows I. Goal J. Data I K. LINDO L. Programs

High Producing Cows I

l. 2. Low Producing Cows 3. Calves 3-6 Months

I

4. Calves 7-12 Months

III MODELS

A. High Producing Cows B. Low Producing Cows C. Calves 3-6 Months D. Calves 7-12 Months

IV TABLES

A. High Producing Cows B. Low Producing Cows C. Calves 3-6 Months D. Calves 7-12 Months I V CONCLUSIONS/RECOMMENDATIONS

I I I I I

[1 I

SCOPE

IThe objective is to maximize the amount and fat content of

the dairy's daily milk production. The methods used will 1 consist of feed-mix formulations. 1 I PURPOSE

The intention of this project is to help the Dairyman

increase the production while at the same time decreasing

his costs to the dairy. This can be done using proper

I methods of Linear Programming within the Feed Mix

processes. IPLAN OF DEVELOPMENT

A majority of the information gathered for this project was

either acquired through information from Mr. David Rankin,

IVice President of Operations of Liberty Financial

Corporation, Norman Dedrick, the on site Dairy Manager of

I Green's Creek Dairy Ltd. and Keith Sliger, the feed salesman

for Moorman's Feed Company. Also, information was gathered I through various magazine articles and dairy science books.

INTENTIONS

IThis report is intended to give a detailed description of

how to optimize the amount of milk and fat content in the

I overall dairy production. Commercial dairy farmers have

found that feed-mix is the most important factor that I I

I I

effects milk quality and quantity. This factor used in the

most optimal manner will yield the maximum profit at a

minimal cost. I I By using individual trait characteristics, dairymen can better evaluate their cows and decide which cows should be

Ibred with which bulls for better offspring and overall

production. Good feeding gives dairymen a physically better

looking cow as well as a cow that can produce more

lactations (capability of being milked per day). This leads I to more profit from the dairy operation (which is the main

objective of the farmer) with less cash out for maintenance I and feed of cows.

The feed that a cow gets is the single most important factor

that determines how much milk as well as fat content that a

cow will produce. In the industry, milk is not measured in 1 gallons, but in pounds (lbs.). The objective, obviously, is

to maximize the amount of milk and fat content (in the

milk) from the cow with as little cost to the dairymen as

possible. I I I I I I

I I

In the dairy industry the percentage of fat in the milk must

be maximized. The fat in the milk is important because the

fat is needed to make the ice-creams, butter and all of the

cheeses which we eat and enjoy today. The more fat that is

in the milk, the more of these products that can be

produced. Also, if the percentage of fat in the milk is

increased, the amount the farmer is paid is increased

(another very important factor). Feed mix is important

here, various mixtures of feed fed to the cows increase or

decrease the amount of fat content in the milk.

We spoke with David Rankin of Liberty Financial on Green's

Creek Dairy Ltd located west of Stephenville Texas in Dublin

on a 1000 head of cattle dairy farm. David is the Senior

Vice President of Operations on location and told us that

the single most important factors in maximizing the output

and fat content of milk from a cow is; what rations of mix you feed your cows.

I PROBLEM David Rankin is a farmer who just began this dairy business

I

a little over 2 years ago. He buys the best feed for his

cattle that he can at the cheapest price. He mixes his feed

Ibecause he realizes that different feeds contain different

vitamins and important nutrients and proteins. The problem

I is, he doesn't have a particular feed-mix program that

employs a feasible solution which will minimize feed cost I 11

while at the same time giving his cattle their daily

nutrient allowance. Basically, he mixes the feed without

considering an optimal feed-mix solution. Cows, depending

on what stages they are in need different amounts of

nutrients for good health. There are milking cows, calves

and bulls -- all of which have to be fed differently.

Following is a list of the various more important nutrients

and vitamins which we used in our feed-mix problems.

Protein is required in a cow's diet to supply amino acids

for its physiological functions. The main importance of

protein is it supplies amino acids to the cow for its

various specific body functions.

The protein requirements of lactating cows are given in two

forms, that of crude protein and that of digestible protein.

Most feeding standards use only crude protein. The

percentage of crude protein of a feed is not constant and

depends primarily on the protein content of the ration.

Because the metabolic fecal nitrogen losses of a cow remain

constant, low levels of protein in the ration result in a

low apparent digestibility, but the amount of protein

digested increases with increased protein percentages in the

ration.

Protein is required for good growth of hooves, hair, horns,

body structure, skin and bones. Protein requirements are

also directly related to the amount of milk produced by the

cow, energy content of the milk and the percentage of fat in

the milk.

FAT

We found information concerning the content of fat in the

feed-mix. Fatty acids such as linoleic, linolenic,

arachidonic acids and choline are essential in the diet of a

milking cow and are found in the fat content of most feeds.

Microorganisms in the cud of the cow can synthesize these

components from carbohydrates in the feed and convert it

into energy in the milk.

In one book (Science of Dairy Farming), it was found in

studies and experiments conducted at Cornell University,

that cows produced more milk when the food mix concentrate

mixture contained 4% or more fat in contrast to rations

containing only 2 or 2.5% fat. The increase in yield was

1.4 pounds of milk per day (and with 1000 head of cattle,

that adds up ), but the problem is that feeds that contain

higher fat contents also cost more and the extra cost

doesn't off-set the money made by producing the extra

percentage of fat in the milk.

ICALCIUM AND PHOSPHOROUS

We learned that calcium and phosphorous are the two most

Iimportant minerals needed in dairy cattle rations because

they are the major components of the skeleton and are two of I

ii II

Ithe most important minerals in milk. There is a better

Ichance of there being a deficiency of phosphorus than

calcium in dairy cow rations because calcium is found in

Ihigh concentrations in hays. But, you have to be careful

because cows that are fed high rations of corn require

Isupplemental (additives) ways of getting calcium because

I

corn is low in calcium. Wheat bran, cottonseed meal, whole

cottonseed and linseed meal are high in phosphorus content.

ICottonseed and whole cottonseed are used on the Green's

Creek Dairy. IThe veterinarian we spoke with at the Dairy told us that the

Isymptoms of phosphorus and calcium deficiencies were very

l

similar. Calcium deficiency results in "mobilization" of

calcium from the bones by the parathyroid glands. Meaning,

Ithe parathyroid glands begins taking the calcium in the

bones of the body of the cow and using it for itself,

Ileaving the bones without the calcium they need to stay

healthy. IIn severe cases of phosphorous and calcium deficiencies, a

I sickness called osteomalacia develops in the animal

I resulting in weak bones that are easily broken and a cow that looks scrawny. On the other hand if there is a

Ideficiency in phosphorus a drop in blood plasma results,

along with a drop in appetite for mature cows and beginning

Iretardation of growth in growing calves.

I I

U I

Large amounts of phosphorus and calcium should be fed to the

1 growing animals and the milk producing cows on a regular

basis. I I The most important thing, though, is the fact that there is a decrease in milk production when there is a lack of these

I

vitamins (phosphorus and calcium) in the cows diet -- milks

main ingredients are calcium and phosphorus.

ISODIUM

I This is the mineral that is least found in dairy farm feed

mixes and is usually added to the cows daily diet through

I additives. Sodium helps the cow to retain its water.

[TiWATER

Even though water is not a specific nutrient, it is the most

critical element in a cows daily intake. It helps in the

transportation of nutrients to the different parts of the

body, in the transportation of waste material to the

kidney, the cow to maintain a constant body temperature and

takes part in all of the chemical reactions that take place

in the body. Cows require 3 or 4 pounds of water for each

pound of milk produced. Their milk production will drop

rapidly if they do not have a sufficient water supply.

DRYING OFF COWS

This is where the dry feed mixture is important. Cows

I should go for a period of from 60 - 120 where they are not

I I I I I Li I

I

Imilked. This gives them a rest before the next lactation

Iperiod, so that they can produce the maximum amount of milk

during the following lactation period. The mammary glands

I gets a rest and the rest period also allows the cow to

replenish her body nutrients and vitamin content. When cows I are producing milk every day, some vital nutrients of the.

cow are used up and hard to retain over a long period of

time. One way is for the farmer to just simply stop milking

Ithe cow so that the udder continues to fill up with milk,

where at some point when a certain pressure is reached

I within the udder, milk secretion is stopped. Another way is

to keep decreasing the amount of milk taken from the cow for

a period of about two weeks and this lets the cow dry up at

a slower pace.

GOAL

Our goal was to feed the various cattle the required

nutrients, proteins and supplements needed while at the same

time decreasing the overall cost of the Dairy's feeding

bill.

DATA

We took the types of feed that Mr. Rankin used at his dairy,

as well as the amount of nutrients (varying percentages) in

Ieach type of feed and the cost per pound (lb) of each

particular feed; alfalfa, barley, cotton seed meal, whole

Icotton seed, Hominy, Malt (wet malt) and the extra additives

that he uses. I I

I I I Instead of trying to solve our Linear Programs by

chose to use the LINDO program which utilizes a

program to to solve Linear Programming models.

hand, we

computer

The following programs objectives are to minimize the cost

of feed-mix, without depriving the cattle of their daily

required nutrients.

Program for high producing cows

A high producing cow is one that produces any where from 70

pounds (approximately 8.14 gallons) and above per day of

milk. The average weight of this group is approximately

1400 pounds. The average fat content in the milk produced

by these high producers is about 4.1%. Of all the cattle

the dairyman owns, this group is his most profitable and

must be well taken care of.

In this model, the objective function variables are

represented by the cost per pound of each of the particular

feeds. The feeds used at the Green's Creek Dairy are as

follows; alfalfa, barley, cottonseed meal, whole cottonseed,

hominy, malt (wet matter) and a special additive. The

constraints used are the minimum requirements of the

nutrients needed. This model has eight nutrient constraints

and seven feed constraints and, two binding constraints.

After entering the data in the LINDO program, we came up

with an optimal solution that would save Green's Creek Dairy

$.18 cents per head of cattle while continuing to give each

cow their daily requirements of vitamins, nutrients and

proteins. The savings, when figured out, for 478 high

producing cows fed for 300 days is $.18 x 478 x 300

= $25,812.00 per year. A substantial savings over their

original cost of $496,164.00 because now, they would be

spending $470,352.00.

I I I I P II

Program for low producing cows

This particular program is similar to that above --

everything remains the same except for the right hand side

which is decreased because the amount of feed needed by

lower producing cattle is less. The savings, when figured

out, for 522 low producing cows fed for 300 days is $.13 x

522 x 300 = $20,358.00 per year. A substantial savings over

their original cost of $472,932.00 because now, they would

be spending $452,574.00 per year.

Program for calves 3 - 6 months

The feeding program designed to replace herd replacements

is considerably different from that designed to raise calves

to be sold at a young age. The initial feed of calves is

important for substantially good frame structure not to

mention their future in the dairy industry as milkers.

Studies have found that there is a direct relationship in

the amount of milk produced by cows which were fed well as

young calves. It is not always the feeding that affects the

I I I I I I L I I I II

I I

calves future production, but sometimes the traits inherited

by the calves sire or mother.

I Since these dairy calves are raised for herd replacements,

I the dairymen are satisfied if their feeding program:

1) Keeps the calves alive

I

2) Keeps the calves healthy

3) Produces heifers who have good appearances

4) Is economical

I The savings, when figured out, for 27 calves fed for 360

days is .07 x 27 x 360 days = $641.00 per year. A I savings over their original cost of $9,332.00 because now,

they would be spending $8,651.00 per year.

IProgram for calves 7 - 12 months

This particular program is similar to that above --I

everything remains the same except for the right hand side

which is decreased because the amount of feed needed by

calves 7 - 12 months old is less then that for the 3 -6

month calves. The savings, when figured out, for 31 head I fed for 300 days is $.04 x 31 x 360 days = $447.00 per year.

I

A savings over their original cost of $15,736.00 because

now, they would be spending $15,289.00 per year.

I I I I

COEFFICIENTS TABLES

INGREDIENTS AL BR CM WC HM ML AD

PROTEIN .18 .11 .41 .22 .08 .06 .11

FIBER .23 .06 .13 .24 .08 .20 .08

CALCIUM .013 .001 .002 --- --- --- .007

PHOSPHORUS .002 .004 .013 .004 .006 .002 .005

SODIUM --- --- --- --- --- --- **

MAGNESIUM --- --- --- --- --- --- **

SULFPJ --- --- --- --- --- --- **

POTASSIUM --- --- --- --- --- --- **

MINIMUM INGREDIENT REQUIREMENT

INGREDIENTS HIGH PRODUCING COW LOW PRODUCING COW

PROTEIN >= 7.280 >= 6.075

FIBER >= 8.740 >= 6.400

CALCIUM >= .306 >= .243

PHOSPHORUS >= .222 >= .162

SODIUM >= .089 >= .061

MAGNESIUM >= .133 >= .081

SULFER >= .089 >= .041

POTASSIUM .>= .488 >= .324

3-6 MONTH CALVES 7-12 MONTH CALVES

PROTEIN >= 1.820 >= 2.900

FIBER )= 1.950 > 3.100

1)

VARIABLE ( AL

BR CM W HM ML 40

OBJECTIVE FUNCTION VALUE

3.28292561

( h MIN 0.07 AL + 0.07 BR s 0.08 CM + 0.07 WC 4 0.06 HM 4- 0.01 ML + 0.18 AD

L SUBJCT -TO H PROTEIN) 0.18 AL + 0.11 BR + 0.41 CM + 0.22 WC 4- 0.08 HM

( 4- 0.06 ML 4 0.11 AD > 7.28 FIBER) 0.23 AL 4- 0.06 BR + 0.13 CM 4- 0.24 WC 4- 0.08 HM

.........O...2..ML+O.O840)= H CALCIUM) 0.013 AL + 0.001 BR + 0.002 CM + 0.007 AD >= 0.306

( H PHOSPHUR) 0.002 AL + 0.004 BR + 0.013 CM + 0.004 WC + 0.006 HM 4- 0.002 ML + 0.005 AD >= 0.222

QO.IUM4 AD •>= -0.-089 --- .. MAGNESM) AD >= 0.133

( .. SULFUR) AD > 0.089 POTASSM) AD >= 0.4P8 AtFALFA) -Al. > 22.5 BARLEY) BR >= 5.34

1 COTMEAL) CM >= 1.4

.WHOICOT) WC >= 3.72 HOMI-N-Y-)-- HM > 4.4 ... .. .

MALT) ML >= 2.4 ( .• ADDITIVE) AD >= 0.9

TOTFFED) Al + BR + CM + WC + HM + ML + AD >= 44.39999 -IO-T.4L-FD1 AL. 4- 3$ +. CM . . 4- WC- +--HM--+--ML- 4- MD - <= 5.3............. END

VALUE REDUCED COST 22.500000 0.000000 5.339999 0.000000 7.161319 .0.000000 3.71.9999 0.000000 4.099999 0.000000 9.2781.81 0.000000 0.900000 0.000000

I I I I I LI

'I LI I LI

MODEL FOR HIGH PRODUCING COWS

( (FILE: FILE FT2IFOO1 A VM/SP (CMS) R3.1 6/12/85 PUT8502

ROW PROTEIN)

FIBER) CALCIUM)

2HCJSPHUR) SODIUM)

MAGNESM) SULFUR)

POTASSM) ALFALFA) BARLEY)

COTMEAL) WHOLC 01)

SLACK OR SURPLUS 2.095835 0.834872 0.012464 0 .000000 0.81.1000 0.767000 0.811000 0.412000 0.000000 0.000000 5.761820 0.000000

DUAL PRICES 0.000000 0.000000 0.000000

-6.363632 0.0 00000 0.000000 0.000000 0.000000

-0.0600.00 -0.047273 0.000000

-0.047273

I I IJ I I

I I

..I .. . .. . . . - -, .. . . .. .,

I

( FILE: A VM/SP (CMS) R3.1 6/12/85 PUTS 502

HOMINY) MALT)

0.000000 6.878181

-0.024545 0.000000

ADDITIVE) 0.000000 -0.150909 TOTFEED.1 8.600006 0.000000 TOTALFD) 0.000000 0.002727

ND.ITERATIONS= 24 -

RANGES

IN WHICH THE BASIS

.. -08-J--COE-F-F-ICIEN•T

IS UNCHANGED

....RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE

COEF INCREASE DECREASE

AL

0.070000 INFINITY 0.060000

BRQ..0700(j.• INFINITY .. 0.047273

CM 0.080000 0.067500 0.015000 WC 0.070000 INFINITY 0.047273 ......... HM 0.060000 INFINITY 0.024545 ML --0.0-1-0000- 0.002308 INFINITY AD 0.180000 INFINITY 0.150909

RIGHIHAND SIDE RANGES

ROW

CURRENT ALLOWABLE . ALLOWABLE RHS INCREASE DECREASE

PROTEIN 7.280000 2.095835 INFINITY FIBER 8.740000 0.834872 INFINITY

--CALCIUM

0.306000- 0.012464 INFINITY PHOSPHUR 0.222000 0.075660 0.063380

SODIUM 0.089000 0.811000 INFINITY MAGNESM 0.133000 0.767000 INFINITY SULFUR 0.089000 .0.811000 INFINITY

POTASSM

0.488000 0.412000 INFINITY ALFALFA 22.500000 6.678181. 0.958736 BARLEY 5.339999 6.559705 5.339999

COTMEAL 1.400000 5.761820 INFINITY WHOLCQT 3.719Q99 8.406664 3.719999 HDMENY 4.099999 8.830375 4.099999

MALT 2.400000 6.878181 INFINITY ADDITIVE 0.900000 8.273505 0.412000 TOTFEED 44.399994 8.600006 INFINITY I TOTALFO 53.000000 31.690002 3.924610

I

MODEL FOR LOW PRODUCING COW

FILE: FILE FT23FOOI A VM/SP (CMS) R3.1 6/12185 PUT8502

• MIN 0.07 Al + 0.07 BR + 0.08 CM + 0.07 WC i- 0.06 HM I 4- 0.01 ML 1- 0.18 Al) SUBJECT TO P ROTEIN) 0.18 AL + 0.11 BR 4 0.41 CM + 0.22 WC + 0.08 HM

• 4 0.06 ML + 0.11 4) >= 6.075 • FIBER) 0.23.L + 0.06 BR + 0.13 CM + 0.24 WC + 0.08 HM • 0.2 ML + 0.08 40 > 6.4

CALCIUM) 0.013 AL + 0.001 BR + 0.002 CM + 0.007 AD >= 0.243 PHOSPHUR.) 0.002 Al + 0.004 BR + 0.013 CM + 0.004 WC + 0.006 HM + 0.002 ML + 0.005 AD >= 0.162

SODIUM) AD >= 0.061 MAGNESM) AD >= 0.081 SULFUR) AD >= 0.041

POTASSM) AT) >= 0.324 I ALFALFA) AL >= 20 BARLEY) BR >= 5.34

COIMEAL) CM = 0 WHOLCOT) WC >= 2.79 I HOMINV) HM >= 3.64

MALT) ML > 2.4 1 ADDITIVE) AD >= 0.9

TOTFEED) AL + BR + CM + WC + HM 4. ML + Al) >= 40.5 TOTALFO) AL + BR CM + WC. + HM 4.-MI + 41) <= 49

END

IOBJECTIVE FUNCTION VALUE

1) 2.89379883

VARIABLE VALUE REDUCED COST I AL 20.000000 0.000000 BR 5.339999 0.000000

--CM . 0.000000 0.000000 I WC HM

2.790000 11.259999

0.000000 0.000000

ML 8.710001 00000000 AD 0..900000 0.0000.00

ROW SLACK OR SURPLUS DUAL PRICES PR0.TE..I-N-)-----_ --0.2-48599 .0•.-000000

FIBER) 1.904799 0.000000 CALCIUM) 0.028640 0.000000

PHOSPHUR) 0.000000 -12.500010 .S.00JUMJ ----. -0.839000 0-.-000000 -.---MAGNESM) 0.819000 0.000000

) SULFUR) 0.859000 0.000000 POTASSM) 0.576000 0.000000 I ALFALFA) ................ ..0.000000 -0.0.60000 BARLEY) 0.000000 -0.035000

) . COTMEAL) 0.000000 0.067500 WHOLCOT) 0.000000 -0.035000

I m FILE: f I LE FT23F001 A VMISP (CMS) R3.1 6/12/R5 PUT8502 HOMINY)

MALT)7.60Q00 6.310001

0.00000 0.00000

ADDITIVE) 0.000000 -0.132500 ...IOIFE,ED .- 8.50.000.0 .0.00.0000

(TOTALFD) 0.000000 0.015000

NO. ITERATIONS= 20

( RANGES IN WHICH THE BASIS IS UNCHANGED ....... .O8J..COEFFJC1N.TR.AN.G.ES

VARIABLE CURRENT ALLOWABLE ALLOWABLE (

ALCOEF INCREASE DECREASE

BR0.070000 INFINITY 0.060000 --..

CM0.070000 •INFIN1.-T_. . 0.0.35.000 0.080000 INFINITY INFINITY WC 0.070000 INFINITY 0.035000 HM

ML-_0.060000 0.070000 0.030000 0.-01.00.00 -. ... 0..0 .1-00_--.. INFI-N1-T-Y 40 0.180000 INFINITY 0.132500

ROW .--.-__- RIGHIHAND SIDE RANGES . CURR-ENT. .- - ALLOWA8tE. A.LCWABL..

-' PROTEINRHS

6.075000INCREASE

0.248599DECREASE INFINITY FIBER

.CALCI.UM ........ 6.400000 0.243.000

1.904799 0.028640 ..-

INFINITY INFI.N.I.fY PHOSPHUR

SODIUM0.162000 0.061000

0.025240 0.839000

0.030480 INFINITY MAGNESM

--SULFUR0.081000 0.041.000

0.819000 0.85.9000

INFINITY INFI.NITY. POTASSM

ALFALFA0.324000

20.0000000.576000 6.310001

INFINITY 2.071654 BARLEY

_-CO TMEAL5.339999 0.000000

12.619991 . .2.770907

5.339999 0.000000 WHOLCOT 2.790000 12.619991 1.657323 HOMINY 3.639999 7.620000 INFINITY MALT

ADDITIVE2.400000 0.90.0000

6.310001 10.15.9997

INFINITY 0.576000 TOTFEED

TOTALFO40.500000 49.000000

8.500000 15.239986

INFINITY 4.206667

I I I I I I

1 I I I I I I I I I

'I I

MODEL FOR CALVES 3 - 6 MONTHS

FILE: F LIE FT26FOO1 A VM/SP (CMS) R3.1 6/12/85 PUT8502

MIN 0.07 AL 4 0.07 BR + 0.07 WC 4 0.06 HM SUBJECT TO

PROTEIN) 0.18 AL + 0.11 BR + 0.22 WC + 0.08 HM >=

FIBER) 0.23 AL + 0.06 BR + 0.24 WC + 0.08 HM >=

ALFALFA) AL >= 6

BARLEY) BR >= 2

WHOLCOT) WC >= •1-.-5 .- •...-. -

HOMINY) HM >= 2.5

TOTFEED) AL + BR + WC + HM >= 13.2

TOTALFD) AL + BR + WC + HM <= 16

END---.- ••...

-1.82 1.95

OBJECTIVE FUNCTION VALUE

1) 0.886999905

VARiABLE VALUE REDUCED COST.. -

ALBR

6.000000 2.000000

0.000000 0.000000

WC 1.500000 0.000000 HM 3.700000 0.000000

ROW SLACK OR SURPLUS DUAL PRICES PROTEIN) 0.106000 0.000000 -

FIBEP) 0.206000 0.000000

ALFALFA)BARLEY)

0.000000 0.000000

-0.010000 -0.010000

W.HQLCOT) .0.000000.. -0.01000.0. HOMINY) 1.200000 0.000000 TOTFEED) 0.000000 -0.060000 TOTALFD) 2.800000 0.000000

NC. ITERATIONS= 3

RANGES IN WHICH THE BASIS IS UNCHANGED

OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE

COEF.. INCREASE DECREASE ............... AL 0.070000 INFINITY 0.010000 BR 0.070000 INFINITY 0.010000 WC 0.070000 INFINITY 0.010000 I HM .0.06.0.000 .

RIGHTHAND

... .0.010000 SIDE RANGES

0.06000.0

ROW CURRENT ALLOWABLE ALLOWABLE . ....R.HS....... . INCR.EAS.E .. DECREASE ...................

PROTEIN 1.820000 0.106000 INFINITY FIBER 1.950000 0.206000 INFINITY

Al 1 C A or, (AflrI1l(1 1 )AAAflr 1 roc1a flL. flL '_J 'flJ'.J'.# !J'J S C_1JW¼''J'J 4. • I,J..J 77 7Q

I JIt -- - FILE: FILE FT26F00I A VM/SP (CMS) R3.1. 6/12/85 P08502

BARLEY 2.000000 1.200000 2.000000 WHOLCOT 1.500000 1.200000 0.757141

HOMINY 2.500000 1.200000 INFINITY TOTFEED 13.200000 . 2.800000 1.200000 TOTALFO 16.000000 INFINITY 2.800000

MODEL FOR CALVES 7 - 12 MONTHS

) F I [E:F1 1E FT28F00'FA VMTSPTCWST R3.V 6] iT85PlJT8.5O2

)r' MI 0.07 AL 4 0.07 BR 4- 0.07 WC + 0.06 HM ; SUBJECT TO LL.R.OIELNL_0Oi 8 ...A.L +O..iiBR_O.22. W.C_.. a...0.&HM>__2. 9 H FIBER) 0.23 AL + 0.06 BR + 0.24 WC 4 0.08 HM >= 3.1 H ALFALFA) AL > 10

BARLEY) BR > 3.5

HOMINY) HM >= 3 TOTFEED) AL + BR + WC + HM >= 20.29999 TOTALFD) AL + BR + WC + HM < 25.2

1) 1.37299824

VARIABLE.................VALUE ----- ----------R-E-DiJCE0--CO-S-T......-..---AL 10.000000 0.000000

.: BR 3.500000 0.000000 I WC 2.000000 0.000000 . . 4.79.9.98.8.__.___.._.. _.O..O0O........-.

IROW SLACK OR SURPLUS DUAL PRICES PRQTEI.N.) ......... .0.-1.0.89-99..--- ...... 0..00.00.0.0.. . .

FIBER) 0.273999 0.000000 ALFALFA) 0.000000 -0.010000 I ;BARLEY) 0.000000 -0.010000

22 1 HOMINY) 1.799988 0.000000 TOTFEED) 0.000000 -0.060000

i' TOTALFD) 4.900009 0.000000 I l 2. L.__ --.-.-. ------------.---.---------.-----.. -..- ------------NO. ITERATIONS 7

I .....-.--- ....----.-.--..

OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE

AL 0.070000 INFINITY 0.010000 )BR Q.fl99Q2

WC INFINITY 0.010000

0.070000 1Nt-1NLY U.UIUUUU

....-------- -O--Ja&0Q-OO

1)3.! RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE

____- - INCREAS.E___.__-__D.EC REAS

I

PROTEIN 2.900000 0.108999 INFINITY FIBER 3.099999 0.273999 INFINITY

ALFALFA 10.000000 1.799988 1.089985

t2l

II FILE: FILE FT28FOOI A

BARLEY 3. 500000 WHOICOT 2.000000

I-I

HOMINY 3.000000 TOF_FED.-- .........2-0.299988- TOTALFO 25. 199997

VMSP (CMS) R3.1 6/12/85 PtJT85O2

1.799988 1.799988 1.799988 4.900009

INFINITY

3.570000 0.7 i8561

INFINITY 1.362481 4.900009

--- ....._ ......,-.....- . .T..............

A

II I I LI Li I I Ip I I [1 I I I

I I

HIGH PRODUCING COWS

Present Feed-Mix Program

FEED LBS/DAY COST/LB TOT. COST

ALFALFA 25 .07 $1.75

BARLEY 6 .07 $ .42

COTTONSEED 5.5 .08 $ .44 MEAL

WHOLE COTTON- 4 .07 $ .28 SEED

HOMINY 4.5 .06 $ .27

MALT 12 .01 $ .12

ADDITIVE 1 .18 .18

TOTAL DAILY COST: $3.46

LINDO FEED-MIX PROBLEM

LBS/DAY COST/LB

22.50 .07

5.34 .07

7.16 .08

TOT. COST

$1.58

$ .37

$ .57

FEED

ALFALFA

BARLEY

COTTONSEED MEAL

WHOLE COTTON-SEED

HOMINY

MALT

ADDITIVE

4.10 .06

9.28 .01

.90 .18

TOTAL DAILY COST:

3.72

07 $ .26

$ .25

$ .09

$ .16

$3.28

LBS/DAY COST/LB

20.00 .07

5.34 .07

0.00 .08

TOT. COST

$1.40

$ .37

$ .00

2.29

07

$ .19

LOW PRODUCING COWS

Present Feed-Mix Prorram

FEED LBS/DAY COST/LB TOT. COST

ALFALFA 25 .07 $1.75

BARLEY 6 .07 $ .42

COTTONSEED 0 .08 $ .00 MEAL

WHOLE COTTON- 4 .07 $ .28 SEED

HOMINY 4.5 .06 $ .27

MALT 12 .01 $ .12

ADDITIVE 1 .18 $ .18

TOTAL DAILY COST: $3.02

LINDO FEED-MIX PROBLEM

FEED

ALFALFA

BARLEY

COTTONSEED MEAL

WHOLE COTTON-SEED

HOMINY

MALT

ADDITIVE

11.26 .06

8.71 .01

.90 .18

TOTAL DAILY COST:

$ .68

$ .09

$ .16

$2.89

LBS/DAY COST/LB

6.00 .07

2.00 .07

0.00 .08

1.50

07

CALVES 3-6 MONTHS OLD

Present Feed-Mix Program

TOT. COST

$ .49

$ .21

$ .00

FEED

ALFALFA

BARLEY

COTTONSEED MEAL

WHOLE COTTON-SEED

HOMINY

MALT

ADDITIVE

2.5 .06

O .01

O .18

TOTAL DAILY COST:

LBS/DAY

COST/LB

7 .07

3 .07

0

08

1.5

07 $ .11

LINDO FEED-MIX PROBLEM

FEED

ALFALFA

BARLEY

COTTONSEED MEAL

WHOLE COTTON-SEED

HOMINY

MALT

ADDITIVE

3.70 .06

0.00 .01

0.00 .18

TOTAL DAILY COST:

$ .22

$ .00

$ .00

$ .89

$ .15

$ .00

$ .00

$ .96

TOT. COST

$ .42

$ .14

$ .00

$ .11

FEED

ALFALFA

BARLEY

COTTONSEED MEAL

WHOLE COTTON-SEED

HOMINY

MALT

ADDITIVE

FEED

ALFALFA

BARLEY

COTTONSEED MEAL

WHOLE COTTON-SEED

HOMINY

MALT

ADDITIVE

I I I I I I I I I I I I I I I I I I I

CALVES 7-12 MONTHS OLD

Present Feed-Mix Program

LBS/DAY

COST/LB

11.0 .07

4.0

07

0.0

08

2.5 • 07

3.0 .06

0.0 .01

0 .18

TOTAL DAILY COST:

LINDO FEED-MIX PROBLEM

LBS/DAY COST/LB

10.00 .07

3.50 .07

0.00 .08

frN'I' .07

4.80 .06

0.00 .01

0.00 .18

TOTAL DAILY COST:

TOT. COST

$ .77

$ .28

$ .00

$ .18

$ .18

$ .00

$ .00

$1.41

TOT. COST

$ .70

$ .24

$ .00

$ .14

$ .29

$ .00

$ .00

$1.3

TOTAL SAVINGS PER YEAR

I

Cattle classification

High Producing Cows

Low Producing Cows

Calves 3-6months old

Calves 7-12months old

TOTAL ANNUAL SAVINGS:

Total

Savings/head Savings

$.18/day $25,812.00

$.13/day $20,358.00

$.07/day $ 641.00

$.04/day $ 447.00

$47,258.00

I I I L I

CONCLUSION/RECOMMENDATION

Our goal was to obtain a feasible feed-mix solution for all

four of the above types of cattle. Through a Linear

Programming model technique known as LINDO, we proved that

there can be a substantial annual savings. Using these

models did not cut any of the daily recommended allowance of

vitamins and nutrients for the cattle.

We recommend that if Green's Creek Dairy wants to save over

$45,000.00 per year, that they use the models discussed in

this technical report.

I I I I I I II I I I I