I built a storage shed in the shape of a rectangular box on a square base. The material that I used for the base cost $4 per square foot, the material for the roof cost $2 per square foot, and the material for the sides cost $2.50 per square foot; and I spent $450 altogether on material for the shed. What should the side of the base be in order to maximize the volume of the shed?

side of 6.124 ft and height of 3.674 ft

Step-by-step explanation:

Let's s be the side of the square base and h be the height of the rectangular box.

The base and the roof would have an area of and cost of

The sides would have an area of 4sh and cost of 4sh*2.5 = 10sh

So the total cost for the material is

The volume of the shed has the following formula

To find the maximum value for V, we can take its first derivative, and set it to 0

h = 45/s - 0.6s = 3.674 ft

you cant answer this dummy

step-by-step explanation: