# The ABC Company is one of the

The ABC Company 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: Hold the capital investment down to no more than \$110 million, Goal 3: Maintain the current employment level of 8,000 employees. All goals are important, but by small margin their order of importance is: Priority 1: Goal 1 Priority 2: Goal 2 Priority 3: Part of Goal 3 (avoid decreasing the employment level) Priority 4: Part of Goal 3 (avoid increasing the employment level) The company estimated contributions per unit of each product to the goals along with all the ngcessary information as follows: (Contributions to the goals per unit of each product) Factor P2 P3 Goal Total profit (Smil) 129152250 Capital investment (Smil) 5 7 8 5 110 Employee level (00s) 153 14 = 80 (Penalty weights measuring the Relative Seriousness of Missing the Goals) Goal Factor Penalty Weight for Missing Goal 1 Total profit 1 7 (per \$1 mil under the goal) 2 Capital investment 5 (per \$1 mil over the goal) 3 Employment level 4 (per 100 employees under the goal) | 2 (per 100 employees over the goal) 1. Formulate the above problem into Goal Programming (GP). 2. Find the optimal solution (Attach the Solver solution).

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