State the Linear Programming Problem in Mathematical Terms, Identifying the Objective

Multiple Choice

State the linear programming problem in mathematical terms, identifying the objective function and the constraints.
-A firm makes products $A$ and B. Product A takes 3 hours each on machine $L$ and machine M; product B takes 3 hours on $L$ and 2 hours on M. Machine $L$ can be used for 13 hours and M for 8 hours. Profit on product $A$ is $\$ 7$ and $\$ 10$ on B. Maximize profit.

A) Maximize $7 \mathrm{~A}+10 \mathrm{~B}$
Subject to: $3 \mathrm{~A}+3 \mathrm{~B} \geq 13$
$2 \mathrm{~A}+3 \mathrm{~B} \geq 8$
$\mathrm{A}, \mathrm{B} \leq 0$ .
B) Maximize $7 \mathrm{~A}+10 \mathrm{~B}$
Subject to: $3 \mathrm{~A}+3 \mathrm{~B} \leq 13$
$2 \mathrm{~A}+3 \mathrm{~B} \leq 8$
$\mathrm{A}, \mathrm{B} \geq 0$ .
C) Maximize $7 \mathrm{~A}+10 \mathrm{~B}$
Subject to: $3 \mathrm{~A}+3 \mathrm{~B} \leq 13$
$3 \mathrm{~A}+2 \mathrm{~B} \leq 8$
$\mathrm{A}, \mathrm{B} \geq 0$ .
D) Maximize $10 \mathrm{~A}+7 \mathrm{~B}$
Subject to: $3 A+2 B \leq 13$
$3 \mathrm{~A}+3 \mathrm{~B} \leq 8$
$\mathrm{A}, \mathrm{B} \geq 0$ .