Fox Enterprises is considering six projects for possible construction over the next four ycars. Fox can undertake any of the projects partially or completely. A partial undertaking of a project will prorate both the return and cash outlays proportionatel; The expected (present value) returns and cash outlays for the projects are given in th following table. Cash outlay ($1000) Project Year ! Year 2 Year 3 Year 4 Return ($1000) 10.5 14.4 2.2 2.4 324.00 8.3 12.6 9.5 3.1 358,00 10.2 14.2 5.6 4.2 177.50 4 7.2 10.5 7.5 5.0 148,00 12.3 10.1 8.3 6.9 6.3 182.00 9.2 7.8 5.1 123.50 Available funds ($1000) 60.0 70.0 35.0 20.0 (a) Formulate the problem as a linear program, and determine the optimal project mix that maximizes the total return using AMPL, Solver, or TORA. Ignore the time value of money. (b) Suppose that if a portion of project 2 is undertaken, then at least an equal portion of project 6 must be undertaken. Modify the formulation of the model, and find the new optimal solution. (c) In the original model, suppose that any funds left at the end of a year are used in the next year. Find the new optimal solution, and determine how much cach ycar "borrows" from the preceding year. For simplicity, ignore the time value of money.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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Fox Enterprises is considering six projects for possible construction over the next
four ycars. Fox can undertake any of the projects partially or completely. A partial
undertaking of a project will prorate both the return and cash outlays proportionatel;
The expected (present value) returns and cash outlays for the projects are given in th
following table.
Cash outlay ($1000)
Project
Year !
Year 2
Year 3
Year 4
Return ($1000)
10.5
14.4
2.2
2.4
324.00
8.3
12.6
9.5
3.1
358,00
10.2
14.2
5.6
4.2
177.50
4
7.2
10.5
7.5
5.0
148,00
12.3
10.1
8.3
6.9
6.3
182.00
9.2
7.8
5.1
123.50
Available funds ($1000)
60.0
70.0
35.0
20.0
(a) Formulate the problem as a linear program, and determine the optimal project mix
that maximizes the total return using AMPL, Solver, or TORA. Ignore the time
value of money.
(b) Suppose that if a portion of project 2 is undertaken, then at least an equal portion
of project 6 must be undertaken. Modify the formulation of the model, and find the
new optimal solution.
(c) In the original model, suppose that any funds left at the end of a year are used in
the next year. Find the new optimal solution, and determine how much cach ycar
"borrows" from the preceding year. For simplicity, ignore the time value of money.

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