# Linear Programming Application

Fairview Manufacturing Company is considering a number of expansion projects to take place over the next four years. Specifically, Fairview Manufacturing needs to utilize a capital budgeting process to select appropriate opportunities from a total of five approved projects under consideration. Each project requires lump sum capital outlays over one or more of the years in the budgeting period where each year is subject to a budgetary (capital) constraint. The objective is to select the set of projects that maximizes a measure of total return on investment (net present value) without violating the capital requirements in each year. Project 1 requires a capital outlay of $300,000 in year 1. Project 2 requires a capital outlay of $500,000 in year 2 and an additional outlay of $100,000 in year 3. Project 3 requires an outlay of $100,000 in year 1, an outlay of $200,000 in year 2, another outlay of $100,000 in year 3, and another outlay of $200,000 in year 4. Project 4 requires an outlay of $1,000,000 in year 1, an outlay of $400,000 in year 2, and an outlay of $200,000 in year 3. Capital outlays for Project 5 consist of an initial outlay of $200,000 in year 1, and outlays of $500,000 and $100,000 in years 3 and 4 respectively. The net present value of benefits for these projects are $200,000, $300,000, $100,000, $500,000, and $400,000 for projects 1 through 5 respectively. Capital available for outlay for these projects are $1,200,000 in year 1, $800,000 in year 2, $800,000 in year 3, and $400,000 in year 4.

Fairview Manufacturing has additional considerations with respect to these projects that must be included in the capital budgeting process: Projects 1 and 3 must be undertaken together, if at all; at most, four projects may be undertaken; Projects 4 and 5 are mutually exclusive and cannot be undertaken together; Projects 2 and 4 are dependent, and if one is undertaken, the other must be as well.

a. Formulate an appropriate linear programming model that can be used to determine the optimal project selection structure for the budgeting period.

b. Determine the optimal project selection using the Management Scientist software, including the projects to included and the total net present value contribution. Provide a narrative that explains the Management Scientist solution used.

https://brainmass.com/math/linear-programming/linear-programming-application-178464

#### Solution Preview

Dear friend,

I go through your line and model the problem as and LP.

"pi" is introduced to be the fraction of project i which is carried out in year t.

1) from "The objective is to select the set of projects that maximizes a measure of total return on investment (net present value)"

and

"The net present value of benefits for these projects are $200,000, $300,000, $100,000, $500,000, and $400,000 for projects 1 through 5 respectively."

Therefore objective is : Max 200 000 p1 +300 000 p2 + 100 000 p3+ 500 000 p4+ 400 000 p5

2)from "without violating the capital requirements in each year." and "Capital available for outlay for these ...

#### Solution Summary

This uses the context of a manufacturing company to use a linear programming model to optimize the situation.