A real-estate development firm, Peterson and Johnson, is considering five possib

Question

A real-estate development firm, Peterson and Johnson, is considering five possible development projects. Using units of millions of dollars, the following table shows the estimated long run profit (net present value) that each project would generate, as well as the amount of investment required to undertake the project. Development Project Estimated proft$1 $1.8 $1.6 $0.8 $1.4 (millions) Capital required6 12 10 4 8 (millions) The owners of the firm, Dave Peterson and Ron Johnson, have raised $20 million of investment capital for these projects. Dave and Ron now want to select the combination of projects that will maximize their total estimated long-run profit (net present value) without investing more than $20 million.

Explanation / Answer

Let Xi = 1 if project i is invested and 0 is project i is not invested

In tabular form

Forming an IP

Max Z = X1 + 1.8 X2 + 1.6 X3 + 0.8 X4 + 1.4 X5

Subjected to 6 X1 + 12 X2 + 10 X3 + 4 X4 + 8 X5

Xi = 1 or 0

Solving binary solution, we get  (X1,X2,X3,X4,X5) = (1, 0, 1, 1, 0) and max z= $3.4 M

X 1 X 2 X 3 X 4 X 5 Estimated Profit (in Mn) 1 1.8 1.6 0.8 1.4 Capital Reqd ( in Mn) 6 12 10 4 8

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