The PC Tech Company assembles and tests two models of computers, Basic and XP. For the coming month, the company wants to decide how many of each model to assemble and test. No computers are in inventory from the previous month, and because these models are going to be changed after this month, the company does not want to hold any inventory after this month. It believes the most it can sell this month are 900 Basics and 1500 XPs. Each Basic sells for $600 and each XP sells for $900. The cost of components for a Basic is $300; for an XP it is $450. Labor is required for assembly and testing. There are at most 10000 assembly hours and 3200 testing hours available. Each labor hour for assembling costs $12 and each labor hour for testing costs $17. Each Basic requires four hours for assembling and one hour for testing, and each XP requires five hours for assembling and two hours for testing. PC Tech wants to maximize its net profit. 1. (8 points) Formulate a linear programming model for this problem. Assume fractional values of the decision variables are allowed.
2. (6 points) Solve this model by using the graphical approach. Indicate clearly the feasible region and the optimal solution on the graph. Report the optimal solution and the optimal objective value. Assume fractional values of the decision variables are allowed. es
3. (3 points) Suppose PC Tech could acquire 100 more hours of testing or assembly but not both. Which would you recommend? What effect would this have on the optimal solution and profit? Give a qualitative answer.
4. (4 points) Suppose that PC Tech realized that it is very difficult to project the maximum number of Basics and XP it can produce, but due to some company requirements, it knows that it needs produce at least 900 Basics and 1500 XPs. What is the new optimal solution?
5. (5 points) If PC Tech could spend $20 per day on advertising that would increase the expected demand for Basic, should it be done?