Simon manufacturing company is preparing to replace its current product line with the next generation of products (P1, P2, and P3). Because of the limited amount of capital available, management needs to make some difficult choices about how much to invest in each of these products. Another concern is the effect of these decisions on the company's ability to maintain a relatively stable employment level. In addressing these decisions, management wants primary consideration given to three goals: total profit, stability in the workforce, and the level of capital investment needed to launch these products. Goal 1: Achieve a total profit of at least $500 million. Goal 2: Maintain the current employment level of 7,000 employees. Goal 3: Hold the capital investment down to no more than $250 million. All goals are important, but their order of importance is: Priority level 1: Goal 1 Priority level 2: Goal 3 Priority level 3: Part of Goal 2 (avoid increasing the employment level) Priority level 4: Part of Goal 2 (avoid decreasing the employment level) The company estimated contributions per unit of each product along with all the necessary information as follows:

Factor P1 P2 P3 Goal Total profit ($mil) 9 12 15 At least $500 mil Employee level (00s) 4 2 3 Maintain 70 employee Capital investment ($mil) 5 7 8 No more than $250 mil Goal Factor Penalty Weight for Missing Goal Goal 1 Total profit 10 (per $1 mil under the goal) Goal 2 Employment level 2 (per 100 employees under the goal 5 (per 100 employees over the goal) Goal 3 Capital investment 8 (per $1 mil over the goal)