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‘WATERWORLD BEVERAGE CAN’. GROUP’S MEMBERS NOR AINI MAT SAMAN NUR HANISAH ABDULLAH NOOR IZZATI TARMIZI INTAN IZAZI CHE ANI. 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.

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Waterworld beverage can

‘WATERWORLD BEVERAGE CAN’

GROUP’S MEMBERS

NOR AINI MAT SAMAN

NUR HANISAH ABDULLAH

NOOR IZZATI TARMIZI

INTAN IZAZI CHE ANI


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
Solution Plan

Step 1

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

Step 2

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


Step 3

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

Step 4

We need to differentiate A to find the critical value


Step 5

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


Step 6

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

If we get >0, its mean the value of r will get the minimum surface area.

Step 7

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


Step 8

So we can find the minimum surface area


Conclusion
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.


6.2cm

12.42cm

Area for circle

Area for rectangle



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