Solve the problem.
-The material for the bottom of a rectangular box costs $\$ 3$ per square foot while the material for the sides and top costs $\$ 1$ per square foot. Find the greatest capacity such a box can have if the total amount available for material is $\$ 12$.
A) $2 \mathrm{ft}^{3}$
B) $3 \mathrm{ft}^{3}$
C) $4 \mathrm{ft}^{3}$
D) $1 \mathrm{ft}^{3}$

Question

Quizplus · Accepted Answer

To maximize the volume, use the cost constraint: $3lw + 2lh + 2wh = 12$. Solving for maximum volume $V = lwh$ with this constraint gives $V = 2 \mathrm{ft}^{3}$.

Solve the Problem $3\$ 3$3 Per Square Foot While the Material for the Sides and Rectangular

Solve the Problem $\$ 3$ Per Square Foot While the Material for the Sides and Rectangular