PLEASE ANSWER ASAP

Question

An open top box with a square base of length x and height y is to be constructed so that its volume is V=3290cm3. If the cost of the material for the base of the box is $0.13 per square centimeter and the cost of the sides is $0.83 per square centimeter, express the cost C of the box in terms of the length of the base x

Answer 1

You will have two equations to start out with.  The first being volume of rectangular prism, and the other being surface area of same figure.

 

x²y = 3290                    eq1     ---->  volume

 

SA = x² + 4xy               eq2

 

SA = x² + 4x(3290 / x²)      

 

SA = x² + (13160 / x)            ---->    surface area in terms of x

 

 

Now we incorporate the cost to eq2 to get a cost formula in terms of x.

 

C = 0.13x² + 0.83(13160/x)