A Western New York semiconductor manufacturer, the Buffalo Chip Company, has in the past had as its principal product the semiconductor logic circuit chips which are used as the building blocks in almost any electronic device. Recently, Buffalo Chip acquired a calculator manufacturing facility which is on an adjacent lot. Each hand-held electronic calculator manufactured by this facility uses 10 circuit chips identical to those produced by Buffalo's chip factory. Very recent price changes make it unclear whether either of both factories are profitable, Chips can be bought for $3 and sold for $2.50 on the market (transportation and handling make the difference). The chip facility has a capacity for 20,000 chips per month. The calculator facility has a capacity for 3,000 calculators per month. The variable cost of producing a chip (including raw materials) is $2. The variable cost of producing a calculator is $20, exclusive of the cost of the 10 chips used per calculator. Each calculator can be sold for $45.

a. Define the decision variables and write the linear program appropriate for maximizing monthly profit contribution.

b. What is the optimal solution? You should be able to determine this by inspection. If the linear program has multiple optimal solutions, identify the optimal solution set.

c. Answer (b) when the price per calculator is set at more than $45 and when is set at less $45.