GROUP’S MEMBERS

NOR AINI MAT SAMANNUR HANISAH ABDULLAH

NOOR IZZATI TARMIZIINTAN IZAZI CHE ANI

‘WATERWORLD BEVERAGE CAN’

Task

As production manager of Waterworld Industry, you need to carry out an investigation on how to minimize the cost of material and hence maximize the profit.

Role

As production manager of Waterworld Industry, we need to determine the dimension of a can that make the minimize cost of materials.

Goal

To find the radius and the height of the cylindrical can when its total surface area is minimum.

Solution Plan

hrV

rrhA2

222

Step 1

2

2

1500

1500

rh

hr

We let the volume of the cylinder is 1.5L, so we can find the h

We know that can is a cylinder, so the formula of cylinder is :

Step 2

We substitute value of h into formula of surface area A,

2

22

23000

21500

2

rr

rr

rA

We need to differentiate A to find the critical value

rrdr

dA 430002

Step 3

Step 4

We need to equal the first differentiate with 0 to find the value of r

cmr

r

r

r

r

rr

2.64

3000

30004

043000

043000

3

3

2

3

2

Step 5

We need to do second derivative to test either the value of r will give the minimum or maximum surface area

4600032

2

rdr

Ad

074.374

2.6

60003 If we get >0, its mean the value of

r will get the minimum surface area.

So we can find the value of h by substitute value of r

cmh 42.12

2.6

15002

Step 6

Step 7

So we can find the minimum surface area

2

2

36.725

2.6242.122.62

cm

A

Step 8

Conclusion

If we want to make a cylindrical can that hold 1.5 L of liquid, we need to use 6.2 cm for radius and 12.42 cm for height hence can minimize the cost of materials.

12.42cm

6.2cm

cm

rnceCircumfere

96.38

2.62

2

Area for circle 2

2

53.241

2.62

cm

Area for rectangle 288.483

96.3842.12

cm

Thank you