In your job at the container factory, you are asked to design a rectangular box with volume 500 cm3 . The material for the sides and bottom costs $0.05 per cm2 while the material for the top costs $0.15 per cm2 . What dimensions do you recommend to minimize the total material cost

6.3 cm by 6.3 cm by 12.6cm

Step-by-step explanation:

Volume of the box=

The minimal dimensions of a box always occur when the base is a square.

Surface Area of a cylinder=

Surface Area of the sides and bottom=

Surface Area for the top =

The material for the sides and bottom costs $0.05 per

The material for the top costs $0.15 per

Therefore Cost of the box

Recall:

The minimum value of C is at the point where the derivative is zero.

The dimensions that would minimize the cost are 6.3 cm by 6.3 cm by 12.6cm

answer is more than one

step-by-step explanation: