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Hint$($s$)$

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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:

Labor$-$Hours Required

$($hours$/$unit$)$ Department Product $1$ Product $2$ Hours Available A $1\mathrm{.}000\mathrm{.}35100$ B $0\mathrm{.}300\mathrm{.}2038$ C $0\mathrm{.}200\mathrm{.}5050$ Profit contribution$/$unit $$30\mathrm{.}00$ $$15\mathrm{.}00$

$($a$)$ Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products $1$ and $2.$ If required, round your answer to two decimal places.

Product $1$ Product $2$ 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 overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime?

What is the upper limit of what you would be willing to pay per hour of overtime in the department you recommended? If required, round your answer to two decimal places. $($c$)$ Suppose that $10,6,$ 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 if 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 $2$ Production

If required, round your answer to nearest whole number. Total Profit $ 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 $0.$

OT hours: Dept. Used A B C

What is the increase in the total contribution to profit if overtime is used? If required, round your answer to nearest whole number.