Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A$,$ B$,$ and C$.$ The labor$-$hour requirements, by department, are as follows:

$($a$)$ Formulate a linear programming model for maximizing total profit contribution.

If the constant is $"1"$ it must be entered in the box. If required, round your answers to two decimal places.

Let $P_1=$ units of product i produced

$($b$)$ Solve the linear program formulated in part $($a$).$ How much of each product should be produced, and what is the projected total profit contribution?

Profit $

are the new objective function and additional equation constraints?

If the constant is $"1"$ it must be entered in the box.

Let $Y_i$ is one if any quantity of product $i$ is produced and zero otherwise.

If required, round your answers to nearest whole number. If your answer is zero, enter $"0".$

Updated Profit $