Denver Transportation Company is considering investing in several projects that have varying capital requirements over the next four years. Faced with limited capital each year, management would like to select the most profitable projects that it can afford. The estimated net present value for each project, the capital requirements, and the available capital over the four-year period are shown in the following binary integer linear programming model.
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Questions
1. What is the optimal solution?
2. What is the total estimated net present value at the optimal solution?
3. Based upon the optimal solution and slack variables, what recommendations could you make to management?
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WhereS = 1 if the store expansion project is accepted; 0 if rejectedF = 1 if the fleet expansion project is accepted; 0 if rejectedM= 1 if the equipment upgrade project is accepted; 0 if rejectedR= 1 if the market research project is accepted; 0 if rejectedand currency is in $1,000s.Maximize75S + 50F + 16E + 12Rs.t.30S + 30F + 10E + 20R ? 8530S + 35F + 20E + 10R? 6040S + 50F + 20E + 10R? 10065S + 55F + 20E + 10R? 125S, F, E, R = 0, 1 (binary)?
What will be an ideal response?
Model | S | F | E | R | Max NetPresent Value |
Store Expansion | Fleet Expansion | Equipment Upgrade | Market Research | ||
Objective Function | 1 | 0 | 1 | 1 | |
Coefficients | $75 | $50 | $16 | $12 | $103 |
Constraints | Resources | Used | Available | ||||
Year 1 Capital | $30 | $30 | $10 | $20 | $60 | ? | $85 |
Year 2 Capital | $30 | $35 | $10 | $10 | $60 | ? | $60 |
Year 3 Capital | $40 | $50 | $20 | $10 | $70 | ? | $100 |
Year 4 Capital | $65 | $55 | $20 | $10 | $95 | ? | $125 |
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