The management of XYZ Corporation 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:

Department	Product (hours/unit) 1 2	Labor-Hours Available
A	1.00 0.38	110
B	0.25 0.30	45
C	0.25 0.45	60
Profit contribution/unit	$30.00 $15.00

What are the optimal (maximum profit) production quantities for the company?

a. What type/s of model/s should be used to solve the problem and why would you use that model/s?

b. Develop a model of the XYZ Corporation problem. Solve the model to determine the optimal product quantities of products 1 and 2.

c. In computing the profit contribution per unit, management did 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 department would you recommend scheduling for overtime? How much would you be willing to pay per hour of overtime in each department?

d. 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?

*The models are discussed in Quantitative Analysis for Management Twelfth Edition by Barry Render. ISBN 978-0-13-350733-1