An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 5

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.
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
b. In computing the profit contribution per unit, management doesn't deduct labor costs because considered fixed for the upcoming planning period. However, suppose, overtime can be scheduled in some of the departments. Which department would you recommend scheduling for overtime? How much would you e willing to pay per hour of overtime in each department?
c. Suppose that 10, 6, and 8 hours of overtime may be scheduled in department A, B and C, respectively. The cost per hour of overtime is $18 in department A, $22.50 in department B, and $12 in department B, $12 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? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?