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
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