In The Name Of Allah Lab 07 ins. Tahani Aldweesh.
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Transcript of In The Name Of Allah Lab 07 ins. Tahani Aldweesh.
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In The Name Of AllahLab 07
ins. Tahani Aldweesh
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LP and Solver
Lab#4
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Lab Objectives
Using Excel’s Solver to solve LP problems
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Problem 2 ( Exercise )How many pounds of oat and corn should be fed to each cattle per day to
minimize feed cost ?
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Step 11-)Decision variables:
-Let X1 be the pounds of oat to be used . -Let X2 be the pounds of corn to be used
2-)Objective Function:
Minimize 5 * X1 + 3 * X2
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Step 1
3 -)Constraints:100 X1 + 100 X2 >= 4000
200 X1 + 400 X2 >= 10000 200 X1 + 100 X2 >= 5000
X1, X2 >= 0
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Step 2
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Step 3
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Problem 2A farmer has 10 acres to plant in wheat and
rye. He has to plant at least 7 acres.he has only $1200 to spend and each acre of
wheat costs $200 to plant and each acre of rye costs $100 to plant.
the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye.
If the profit is $500 per acre of wheat and $300 per acre of rye
how many acres of each should be planted to maximize profits?
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Step 11-)Decision variables :
Let x = the number of acres of wheatand y = the number of acres of rye.
2-)Objective Function:
Profit max= 500x + 300y
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3-)Constraints:
X + Y <= 10 X + Y <= 7
200X + 100 Y <= 1200
X + 2Y <= 12
X>=0 , Y >=0
area
Cost
Time
Non Negative Value
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Problem 3A gold processor has two sources of gold ore, source
A and source B. In order to keep his plant running, at least three tons
of ore must be processed each day. Ore from source A costs $20 per ton to process, and
ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day. Moreover, Federal Regulations require that the
amount of ore from source B cannot exceed twice the amount of ore from source A.
If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton .
how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints?
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1 .Define the unknownsLet x = the number of tons from source Aand y = the number of tons from source B
2 .Express the objectiveThe objective is to maximize the amount of the gold yield. Since each ton of ore from source A yields 2oz. of gold and each ton of ore from source B yields 3oz. of gold, the amount of gold recovered will be
Profit max = 2x + 3y
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3 .Express the constraintsAfter getting the unknowns and the objective out of the way, everything else in the problem is a constraint. The constraints are the
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X + Y >= 3
20X + 10 Y <= 80
Y <= 2X
X , Y >= 0
Processing
Costfederal
regulations
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Bryant's Pizza, Inc. is a producer of frozen pizza products.
The company makes a net income of $1.00 for each regular pizza and $1.50 for each deluxe pizza produced.
The firm currently has 150 pounds of dough mix and 50 pounds of topping mix.
Each regular pizza uses 1 pound of dough mix and 4 ounces (16 ounces= 1 pound) of topping mix.
Each deluxe pizza uses 1 pound of dough mix and 8 ounces of topping mix.
Based on the past demand per week, Bryant can sell at least 50 regular pizzas and at least 25 deluxe pizzas.
Problem 4
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The problem is to determine the number of regular and deluxe pizzas the company should make to maximize net income. Formulate this problem as an LP problem.
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1 .Define your unknownsX1 be the number of regular pizzaX2 be the number of deluxe pizza
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2 .Express the objectiveMaximize X1 + 1.5 X2
3 .Express the constraints Subject to:X1 + X2 <=150 (dough mix ) 0.25 X1 + 0.5 X2 <= 50 (Topping mix ) X1 >= 50X2 >= 25X1 >=0, X2 >= 0
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Any Question
ins. Tahani Aldweesh