Solve the problem.
-A company wishes to manufacture a box with a volume of 16 cubic feet that is open on top and is twice as long as it is wide. Find the width to the nearest foot of the box that can be produced using the minimum amount of material.
A) $4 \mathrm{ft}$
B) $3 \mathrm{ft}$
C) $2 \mathrm{ft}$
D) $6 \mathrm{ft}$

Question

Quizplus · Accepted Answer

To minimize the material, we need to minimize the surface area. Let width = w, length = 2w, and height = h. Volume = w * 2w * h = 16, so h = 8/w^2. Surface area = w * 2w + 2(w * h) + 2(2w * h). Substitute h and minimize the function. The minimum occurs at w = 2 ft.

Solve the Problem 4ft4 \mathrm{ft}4ft B) 3ft3 \mathrm{ft}3ft C) 2ft2 \mathrm{ft}2ft D) 6ft6 \mathrm{ft}6ft

Solve the Problem $4 \mathrm{ft}$ B) $3 \mathrm{ft}$ C) $2 \mathrm{ft}$ D) $6 \mathrm{ft}$