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What are the optimal product quantities? What is the revised total contribution to profit? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?

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 $17 in department A,
$21.50 in department B, and $10 in department C.

Formulate a model that can be used to determine the optimal production quantity if overtime is made available. What are the optimal product quantities? What is the revised total contribution to profit? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?

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