CompLounge Industries produces three different models of recliners. All three have a computer and keyboard installed in the left arm. Installed in the right arm, Model 234 has a telephone, Model 450 has a small refrigerator (for drinks), and Model 815 has a smaller refrigerator and a keypad that can be used as both a telephone and a remote control. The models are sold to retailers for $1500, $2000, and $2200, respectively.
CompLounge produces some recliners itself but also contracts with independent manufacturers (Lazyman, Relaxer, and BeatComp) to fill its orders. The following table gives the cost to CompLounge for each model. For the upcoming month CompLounge has orders for 300 Model 234s, 250 Model 450s, and 500 Model 815s.
a. If it takes roughly the same amount of time to produce each type of chair, and production capacities at the four plants are 400, 375, 275, and 125 per month, respectively, how should production be scheduled at the plants this month? What is the minimum total cost to CompLounge? What will be its total profit?
b. Suppose that resources at the independent manufacturers (LazyMan, Relaxer, and SeatComp) are such that the maximum number of Model 450s that can be produced are 75, 100, and 50, respectively, and the maximum number of Model 815s that can be produced are 125, 150, and 25, respectively. Now, how should production be scheduled at the plants this month? What is the minimum total cost to CompLounge? What will be its total profit?