Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows:
- Category Product 1 Product 2 Product 3
- Profit/unit $30 $50 $20
- Machine 1 time/unit 0.5 2.0 0.75
- Machine 2 time/unit 1.0 1.0 0.5
Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2 time. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced.
a) Formulate a linear programming model that can be used to determine the number of units of each product to produce to maximize the total profit contribution.
b) What is the optimal solution, and what is the projected weekly profit associated with your solution?
c) How many hours of production time will be scheduled on each machine?
d) What is the value of an additional hour of labor?
e) Assume that labor capacity can be increased to 120 hours. Would you be interested in using the additional 20 hours available for this resource? Develop the optimal production mix assuming the extra hours are made available.