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: Product 1 Product 2 Product 3. Category 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. 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) How many units of each product should be produced to maximize the total profit contribution? What is the projected weekly profit (in $) associated with your solution? Product 1 Product 2 Product 3 weekly profit (b) How many hours of production time will be scheduled on each machine? machine 1 machine 2 hr hr (c) What is the value (in $) of an additional hour of labor? (d) Assume that labor capacity can be increased to 160 hours. Develop the optimal product mix and the projected weekly profit (in $), assuming the extra hours are made available. Product 1 Product 2 Product 3 weekly profit Would you be interested in using the additional 60 hours available for this resource? Yes, the weekly profit would be increased. No, the weekly profit would be decreased.