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GMCO produces three types of cars: compact, medium, and large. The variable cost per car and production capacity (per year) for each type of car are given in the data to the left. The annual demand for each type of car depends on the prices of the three types of cars, also given in this file. In this latter table, PC is the price charged for a compact car (in thousands of dollars). The variables PM and PL are defined similarly for medium and large cars. Suppose that each compact car gets 32 mpg, each medium car gets 25 mpg, and each large car gets 16 mpg. GMCO wants to keep the planet pollution free, so in addition to maximizing profit, it wants to maximize the average miles per gallon attained by the cars it sells. Construct a trade-off curve between these two objectives. Your submittal must be the the model and solution that answers the question. Be sure to show a table and trade off curve of at least 5 points between the optimal trade off points.

Variable costs and production capacities \begin{tabular}{l|l|r} \hline & & Cost \\ \hline & Compact & $10,000 \\ \hline & Medium & $14,000 \\ 7 & Large & $18,000 \\ \hline & & \\ \hline & Demand functions \\ \hline 0 & Compact & 2500100PC+3PM \\ \hline & Medium & 210030PM+2PC+PL \\ \hline 2 & Large & 150020PL+PM \end{tabular}