Question 2

An electronic manufacturer intends to maximize profit. The manufacturer produces six devices used in computers: internal modems (xA), external modems (xB), graphics circuit boards (xC), USB memory stick (xD), hard disk drives (xE), and memory expansion boards (xF). Demand is expected to be within 2,000, 1,500, 1,800, 1,200, 1,000 and 1,000 units of each of the electronic devices produced, respectively. The table that follows summarizes the revenues and material costs for each product:

Each of these devices needs to be tested before being sold. Specifically, each device needs to go through three different tests. The three tests are performed using different electronic testing equipment, T1, T2 and T3. Equipment T1 and T2 are available 130 hours per week each, while T3 is available only 100 hours per week. The time (in minutes) required per device for each of the three tests is reported in the following table:

Finally, operating the testing equipment requires specialised personnel and it is therefore costly. The variable labour costs are $16 per hour for equipment T1, $12 per hour for T2, and $18 per hour for T3.

A) Write a linear program for this problem and find a solution Excel Solver. (Hint: pay particular attention to determine the objective function)

B) Suppose that the manufacturer is considering to increase only the available time for testing equipment T2. What would be the increase in the profit if the available time increased to 131, 132, 133, 134 and 135? Can you generalise the answer to part C for any increase 130+t where t is between 1 and 10? What would the formula r profit increase be?

C) Should the manufacturer consider increasing the available time for testing equipment T3?