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Brooks Development Corporation (BDC) faces the following capital budgeting decision. Six real estate projects are available for investment. The net present value and expenditures required for each project (in millions of dollars) are as follows. There are conditions that limit the investment alternatives: Project Net Present Value ($ millions) $17 $7 $15 $16 Expenditure Required ($ millions) $94 $38 $85 $74 $118 $54 Max s.t. i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars. The budget for this investment period is $220 million. (a) Formulate a binary integer program that will enable BDC to find the projects to invest in to maximize net present value, while satisfying all project restrictions and not exceeding the budget. (Let x; = if project i is undertaken for 0 otherwise • At least two of projects 1, 3, 5, and 6 must be undertaken. • If either project 3 or 5 is undertaken, they must both be undertaken. • Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken. constraint on projects 1, 3, 5, and 6 constraint on projects 3 and 5 constraint on projects 1 and 4 3 constraint on projects 3 and 4 budget constraint 5 million $22 $11 (b) Solve the model formulated in part (a). What is the optimal net present value (in millions of dollars)? $ How much of the budget is unused (in millions of dollars)? $ million Which projects will be undertaken? (Enter your answer as a comma separated list of numbers. Use 1 for project 1, 2 for project 2, 3 for project 3, 4 for project 4, 5 for project 5, and 6 for project 6.)

Brooks Development Corporation (BDC) faces the following capital budgeting decision. Six real estate projects are available for investment. The net present value and expenditures required for each project (in millions of dollars) are as follows. There are conditions that limit the investment alternatives: Project Net Present Value ($ millions) $17 $7 $15 $16 Expenditure Required ($ millions) $94 $38 $85 $74 $118 $54 Max s.t. i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars. The budget for this investment period is $220 million. (a) Formulate a binary integer program that will enable BDC to find the projects to invest in to maximize net present value, while satisfying all project restrictions and not exceeding the budget. (Let x; = if project i is undertaken for 0 otherwise • At least two of projects 1, 3, 5, and 6 must be undertaken. • If either project 3 or 5 is undertaken, they must both be undertaken. • Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken. constraint on projects 1, 3, 5, and 6 constraint on projects 3 and 5 constraint on projects 1 and 4 3 constraint on projects 3 and 4 budget constraint 5 million $22 $11 (b) Solve the model formulated in part (a). What is the optimal net present value (in millions of dollars)? $ How much of the budget is unused (in millions of dollars)? $ million Which projects will be undertaken? (Enter your answer as a comma separated list of numbers. Use 1 for project 1, 2 for project 2, 3 for project 3, 4 for project 4, 5 for project 5, and 6 for project 6.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Brooks Development Corporation (BDC) faces the following capital budgeting decision. Six real estate projects are available for investment. The net present value and expenditures required for each project (in millions of dollars) are as follows. Project 2 3 4 5 6 Net Present Value ($ millions) $17 $7 $15 $16 $22 $11 Expenditure Required ($ millions) $94 $38 $85 $74 $118 $54 There are conditions that limit the investment alternatives: The budget for this investment period is $220 million. (a) Formulate a binary integer program that will enable BDC to find the projects to invest in to maximize net present value, 1 if project i is undertaken while satisfying all project restrictions and not exceeding the budget. Let x, = 0 otherwise for Max • At least two of projects 1, 3, 5, and 6 must be undertaken. • If either project 3 or 5 is undertaken, they must both be undertaken. ● Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken. i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars. s.t. constraint on projects 1, 3, 5, and 6 constraint on projects 3 and 5 1 constraint on projects 1 and 4 constraint projects 3 and 4 budget constraint (b) Solve the model formulated in part (a). What is the optimal net present value (in millions of dollars)? $ million Which projects will be undertaken? (Enter your answer as a comma separated list of numbers. Use 1 for project 1, 2 for project 2, 3 for project 3, 4 for project 4, 5 for project 5, and 6 for project 6.) How much of the budget is unused (in millions of dollars)? $ million
Transcribed Image Text:Brooks Development Corporation (BDC) faces the following capital budgeting decision. Six real estate projects are available for investment. The net present value and expenditures required for each project (in millions of dollars) are as follows. Project 2 3 4 5 6 Net Present Value ($ millions) $17 $7 $15 $16 $22 $11 Expenditure Required ($ millions) $94 $38 $85 $74 $118 $54 There are conditions that limit the investment alternatives: The budget for this investment period is $220 million. (a) Formulate a binary integer program that will enable BDC to find the projects to invest in to maximize net present value, 1 if project i is undertaken while satisfying all project restrictions and not exceeding the budget. Let x, = 0 otherwise for Max • At least two of projects 1, 3, 5, and 6 must be undertaken. • If either project 3 or 5 is undertaken, they must both be undertaken. ● Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken. i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars. s.t. constraint on projects 1, 3, 5, and 6 constraint on projects 3 and 5 1 constraint on projects 1 and 4 constraint projects 3 and 4 budget constraint (b) Solve the model formulated in part (a). What is the optimal net present value (in millions of dollars)? $ million Which projects will be undertaken? (Enter your answer as a comma separated list of numbers. Use 1 for project 1, 2 for project 2, 3 for project 3, 4 for project 4, 5 for project 5, and 6 for project 6.) How much of the budget is unused (in millions of dollars)? $ million
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