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Better Products, Inc., manufactures three products. Each product has to run through all three machines sequentially. In a typical week, 36 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 $35 Machine 1 time/unit 1.25 1.75 1 Machine 2 time/unit 1.0 1.0 0.75 Machine 3 time/unit 0.75 0.75 1.25

Only one operator is required for machine 1. Two operators are required for machine 2; thus, 2 hours of labor must be scheduled for each hour of machine 2. The same applies to machine 3 which requires two operators to operate this machine; hence, 2 hours of labor must be scheduled for each hour of machine 3. A maximum of 148 labor-hours is available for assignment to operators to work on the machines during the coming week. Other production requirements are that product 1 must account for at least 40% of all units produced and product 2 cannot be more than 25% of the units produced from products 1 and 3.

a. From your optimal solution, what is your product mix and its associate projected weekly profit? b. From the results of both machine hours used and labor hours used, which one should the company increase in the event they want to increase the production capacity? Give your justifications. c. What is the value of an additional hour of labor in terms of its contribution to the total profit? Interpret the results. From the results, do you recommend the company to increase labor and if so by how much? d. Better Products management wants to make changes (increase capacity) to the other production requirement for either product 1 or product 2 that will impact the profit. Using the current optimal solution of production mix, which product would you recommend the management change and by how much. Give justifications for your recommendation.