An auto manufacturer produces two versions of its flagship sedan, one with an automatic transmission (A) and one with a manual transmission (M). The manufacturer can make a profit of $40,000 for each A version sold and $20,000 for each M version sold. Each version is made with two types of labor, assembly labor and finishing labor. Automatic cars require 20 labor hours of assembly and 30 labor hours of finishing. The manual version requires 20 labor hours of assembly and 10 hours of finishing. The goal of the manufacturer is to maximize profit given the following three daily production constraints: 1. The manufacturer can produce a maximum of 100 automatic transmissions per day. 2. The manufacturer can employ a maximum of 6,000 labor hours for assembly per day. 3. The manufacturer can employ a maximum of 4,200 labor hours for finishing per day
(b) Illustrate the constraints on a graph with manual cars (M) on the y-axis and automatic cars (A) on the x-axis and specify the feasible region. (Hint: Rewrite the constraints in a way that can be easily graphed in M-A space.)