Question $3(6$ marks$)$

Rad Inc. makes two boats in addition to their regular fleet. These two boats, the AFQ$3$ and ABQ$7,$ can be special ordered and the company will occasionally offer them for sale without orders when the company resources permit their production. In total $2400$ machine$-$hours are available for making both products. The AFQ$3$ requires $4$ hours per unit and the ABQ$7$ requires $6$ hours per unit. Also available are $1600$ person$-$hours for painting the products. The respective number of person$-$hours required for painting the AFQ$3$ and ABQ$7$ are $2$ and $4$ respectively. The company has orders for $240$ units of the A$-$Fly. Each AFQ$3$ contributes $$250$ to company profits while the ABQ$7$ contributes $$320$ to company profits.

a$.$ State the objective function and the constraints related to the above conditions. $3$ marks

b$.$ Sketch the constraints to this linear programming problem, determine the points that make the feasible region and the optimal number of A$-$Fly and B$-$Fly. $($Show your calculations$).3$ marks