Question: (a) A firm produces small and medium television sets. The profit is 400 for each small and 500 for each medium television set. Each television has to be processed on three different assembly lines. Each small television requires respectively 2, 1, and 1 hour on lines 1, 2, and 3. The corresponding numbers for the medium television sets are 1, 4, and 2. Suppose lines 1 and 2 both have a capacity of at most 16 hours per day, and line 3 has a capacity of at most 11 hours per day. Let x1 and x2 denote the number of small and medium television sets that are produced per day. Show that in order to maximize profits per day, one must solve the following problem:
(b) Solve this problem graphically.
c) Suppose the firm could increase its capacity by 1 hour a day on just one of its assemply lines. Which line should have its capacity increased?