The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:

search n

Labor Hours Required

nours unte

Department

Product $1$ Product $2$ Hours Available

$1\mathrm{.}00$

$0\mathrm{.}35$

$100$

$38$

Pront coninbuton unit

$$30\mathrm{.}00$

$$15\mathrm{.}00$

$($a$)$ Develop a linear programming model or te Harman company problem. solve the model to determine the opamal producion quandues or produces tand $2$

It required. round vour answer to two decimal places

Product Product?

Production

$($b$)$ In computing the profit contribution per unit, management does not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overume can be scheduled in some of the

departments. which desartments would you recommend scheduling for overume

What is the unner limit of what you would be willing to day per hour of overtime in the department you recommended?

If required, round your answer to two decimal places.

$($C$)$ Suppose that $8,6,$ and $8$ hours of overtime may be scheduled in departments A$,$ B$,$ and C$,$ respectively. The cost per hour of overtime is $$18$ in department A$,$ $$22\mathrm{.}50$ in department B$,$ and $$12$ in department C$.$ Formulate a linear programming model that can be used to determine the optimal production quantities it overtime is made available. What are the optimal production quantities, and what is the revised total contribution to profit?

If required, round your answer to two decimal places.

Product $1$ Product

Production

It required, round your answer to nearest whore number

Total Profit S

How much overtime do you recommend using in each department?

If required, round your answer to two decimal places. If you answer Is zero, enter u

OT hours:

Dept.

Used.

A

B

C