solution

The ABCCompany is one of the largest producers of power tools in the United States. The company is preparing to replace its current product line with the next generation of products: specifically, three exciting new power tools with the latest state-of-the-art features. 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 factors: total profit, stability in the workforce, and the level of capital investment needed to launch these products.

Goal 1: Achieve a total profit (NPV) of at least $250 million.

Goal 2: Maintain the current employment level of 8,000 employees. Goal 3: Hold the capital investment down to no more than $110 million.

All goals are important, but by small margin their order of importance is: Priority 1: Goal 1,

Priority 2: Goal 3,

Priority 3: Part of Goal 2 (avoid increasing the employment level), Priority 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 ($mil)	12	9	15	= 250
Employee level (00s)	5	3	4	= 80
Capital investment ($mil)	5	7	8	= 110

Goal	Factor	Penalty Weight for Missing Goal
1	Total profit	50 (per $1 mil under the goal)
2	Employment level	20 (per 100 employees under the goal 30 (per 100 employees over the goal)
3	Capital investment	40 (per $1 mil over the goal)

1. Formulate the above problem into Goal Programming (GP).
2. Find the optimal solution (Attach Excel file).