Brooks Development Corporation (BDC) faces the following capital budgeting decision. Six real estate projects are available forinvestment. The net present value and expenditures required for each project (in millions of dollars) are as follows.Project2 3 4 5 6Net Present Value ($ millions)$17 $7$15 $16 $22 $11Expenditure Required ($ millions) $94 $38 $85 $74 $118 $54There are conditions that limit the investment alternatives:The budget for this investment period is $220 million.(a) Formulate a binary integer program that will enable BDC to find the projects to invest in to maximize net present value,1 if project i is undertakenwhile satisfying all project restrictions and not exceeding the budget. Let x, =0 otherwiseforMax• At least two of projects 1, 3, 5, and 6 must be undertaken.• If either project 3 or 5 is undertaken, they must both be undertaken.●Project 4 cannot be undertaken unless both projects 1 and 3 also are undertaken.i = 1, 2, 3, 4, 5, 6. Give your objective function in millions of dollars.s.t.constraint on projects 1, 3, 5, and 6constraint on projects 3 and 51constraint on projects 1 and 4constraint projects 3 and 4budget constraint(b) Solve the model formulated in part (a). What is the optimal net present value (in millions of dollars)?$millionWhich projects will be undertaken? (Enter your answer as a comma separated list of numbers. Use 1 for project 1, 2 forproject 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

Linear programming helps us to find the optimal solution/best outcome, with the given constraints.…

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.)

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 46P