Extel Industries produces integrated circuit components for use in the next generation of automobiles. In particular, it can make the AT50 unit that can control the air temperature in the car, the V35 unit that monitors vibration and makes adjustments accordingly, and the GM30 that regulates the engine so that the car provides maximum efficiency. The unit profits on these units are $84, $112, and $126, respectively. Each of these units uses different quantities of three computer chips (as shown below), which Extel purchases from a Taiwanese distributor.

C101 H122 P043
AT50 1 1 1
V35 1 1 2
GM30 1 2 1

a. Formulate a linear programming model to help Extel decide how many units of each product to produce weekly. Provide your formulation, define decision variables, provide your objective function using your variables (not in words), provide the constraints as equalities or inequalities expressed using your variables (not in words), and provide the optimal production schedule.

b. Taiwanese distributor informed Extel that they will send 50 more chips free of charge (it is a company policy to award loyal customers). The only restriction is that all 50 have to be the same type of chip, (i.e. no mixing allowed). Which chip do you choose? Why?

c. If the profit for the first unit, AT50, drops to $50, how does your plan change?