The Erlanger Manufacturing Company makes two products. The profit estimates are $35 for each unit of product 1 sold and $50 for each unit of product 2 sold. The labor-hour requirements for the products in the three production departments are shown in the following table.
Product
Department 1 2
A 1.50 3.00
B 2.00 1.00
C 0.25 0.25
The departments' production supervisors estimate that the following number of labor-hours will be available during the next month: 450 hours in department A, 325 hours in department B, and 50 hours in department C.
a. Develop a linear programming model to maximize profits.
b. Find the optimal solution. How much of each product should be produced, and what is the projected profit?
c. What are the scheduled production time and slack time in each department?