Better Products, Inc., manufactures three products on three 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:

Two operators are required for machine 1 and 2 hours of labor must be scheduled for each hour of machine 1 time. The same applies to machine 3 which requires two operators to operate this machine and 2 hours of labor must be scheduled for each hour of machine 3.

Only one operator is required for machine 2. A maximum of 144 labor hours is available for assignment to operators working on 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 30% of the units produced. Develop an optimal product mix on Excel using linear programming.

CategoryProduct 1Product 2Product 3

Profit/Unit$30$50$20

Machine 1 time/unit0.5 2.00.75

Machine 2 time/unit1.0 1.0 0.75

Machine 3 time/unit1.0 1.5 1.0

1. How many units of each product should be produced to maximize the total profit contribution?
2. What is the projected weekly profit associated with your solution?