The Manny Company is producers of electrical tools in the England. The company is preparing to...

 

Transcribed Image Text:

The Manny Company is producers of electrical tools in the England. The company is preparing to replace its current product line with the next generation of products-three new electrical tools. Manager requires to see the mix of the company's three new products to best meet the following three goals 1. Maximize the total profit (net present value) of at least $120 million. 2. Maintain the current employment level of 4000 employees. 3. Hold the capital investment down to no more than $50 million. It will not be possible to attain all these goals simultaneously. All goals are important but by small margins their order of importance is: Goal 1, part of Goal 2 (avoid decreasing the employment level), Goal 3, part of Goal 2 (avoid increasing the employment level), Goal 1: Total profit. Penalty Weight for Missing Goal: 5 (per $1 million under the goal) Goal 2: Employment level. Penalty Weight for Missing Goal: 4 (per 100 employees under the goal) and 2 (per 100 employees over the goal) Goal 3: Capital investment. Penalty Weight for Missing Goal: 3 (per $1 million over the goal) Unit Contribution of Product Factor Total profit (millions of dollars) Employment level (hundreds of employees) Capital investment (millions of dollars) 1 2 3 Goal 12 9 152 120 5 3 4 = 40 5 7 8 ≤ 50 Write a Preemptive Goal Programming Formulation for the problem (8 pt) and solve it using simplex method (17 pt). Show all solution tables The Manny Company is producers of electrical tools in the England. The company is preparing to replace its current product line with the next generation of products-three new electrical tools. Manager requires to see the mix of the company's three new products to best meet the following three goals 1. Maximize the total profit (net present value) of at least $120 million. 2. Maintain the current employment level of 4000 employees. 3. Hold the capital investment down to no more than $50 million. It will not be possible to attain all these goals simultaneously. All goals are important but by small margins their order of importance is: Goal 1, part of Goal 2 (avoid decreasing the employment level), Goal 3, part of Goal 2 (avoid increasing the employment level), Goal 1: Total profit. Penalty Weight for Missing Goal: 5 (per $1 million under the goal) Goal 2: Employment level. Penalty Weight for Missing Goal: 4 (per 100 employees under the goal) and 2 (per 100 employees over the goal) Goal 3: Capital investment. Penalty Weight for Missing Goal: 3 (per $1 million over the goal) Unit Contribution of Product Factor Total profit (millions of dollars) Employment level (hundreds of employees) Capital investment (millions of dollars) 1 2 3 Goal 12 9 152 120 5 3 4 = 40 5 7 8 ≤ 50 Write a Preemptive Goal Programming Formulation for the problem (8 pt) and solve it using simplex method (17 pt). Show all solution tables