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 Net Present Value ($ millions) $19 $9 $17 $18 $24 $13 Expenditure Required ($ millions) $93 $37 $84 $73 $117 $53 There are conditions that limit the investment alternatives: Max s.t. 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 x₁ = (Let x, = {1 If project / is undertaken for i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars.) • 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 1 2 3 4 5 6 constraint on projects 3 and 5 constraint on projects 1 and 4 constraint on 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
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 Net Present Value ($ millions) $19 $9 $17 $18 $24 $13 Expenditure Required ($ millions) $93 $37 $84 $73 $117 $53 There are conditions that limit the investment alternatives: Max s.t. 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 x₁ = (Let x, = {1 If project / is undertaken for i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars.) • 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 1 2 3 4 5 6 constraint on projects 3 and 5 constraint on projects 1 and 4 constraint on 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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 46P
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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.
There are conditions that limit the investment alternatives:
Max
Project
$19 $9
$18
Net Present Value ($ millions)
Expenditure Required ($ millions) $93 $37 $84 $73
budget. Let x;
s.t.
=
constraint on projects 1, 3, 5, and 6
1
constraint on projects 3 and 5
constraint on projects 1 and 4
2
constraint on projects 3 and 4
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
1 if project i is undertaken for i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars.
0 otherwise
budget constraint
3
• At least two of projects 1, 3, 5, and 6 must be undertaken.
either project 3 or 5 is undertaken, they must bot be un
ken.
Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken.
4
$17
5
How much of the budget is unused (in millions of dollars)?
million
6
$24
$117 $53
$13
(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.)
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