The Erlanger Manufacturing Company makes two products. The profit estimates are $25 for each unit of product 1 sold and $30 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, 350 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?