GROUP’S MEMBERS NOR AINI MAT SAMAN NUR HANISAH ABDULLAH NOOR IZZATI TARMIZI INTAN 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 Step 1 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, We need to differentiate A to find the critical value Step 3 Step 4

We need to equal the first differentiate with 0 to find the value of r Step 5

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. So we can find the value of h by substitute value of r Step 6 Step 7

So we can find the minimum surface area 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 cm for height hence can minimize the cost of materials.

12.42cm 6.2cm Area for circle Area for rectangle

Thank you