7.5 A real-estate development firm, Peterson and Johnson, is considered 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 operate as well as the amount of investment required to undertake the project.

Development Project
	1	2	3	4	5
Estimated profit (millions)	$1	$1.8	$1.6	$0.8	$1.4
Capital required (millions)	6	12	10	4	8

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.

Formulate a BIP model in algebraic form for this problem.

Formulate and solve this model on a spreadsheet. What projects should be selected in order to maximize the expected long-term profit? What would the maximum profit be?

Perform sensitivity analysis on the amount of investment capital made available for the development projects by generating a parameter analysis report with RSPE to solve the model with the following amounts of investment capital (in millions of dollars): 16, 18, 20, 22, 24, 26, 28, and 30. Include both the changing cells and the objective cell as output cells in the parameter analysis report. Describe how the optimal solution and objective function value change with the change of investment capital available.