Solve.
-A rectangular box with volume 468 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base in feet. Express the cost of the box as a function of x and then graph this function. From the graph find the value of x, to the nearest hundredth of a foot, which will minimize the cost of the box.
A)8.63 feet
B)8.44 feet
C)7.92 feet
D)8.55 feet

Question

Quizplus · Accepted Answer

The cost function is derived from the surface area of the box. The volume constraint gives the height as a function of x. The cost function is minimized using calculus or graphing, resulting in approximately 8.55 feet.

Solve. -A Rectangular Box with Volume 468 Cubic Feet Is Built