1. Fox Enterprises is considering six projects for possible construction over the next four years. The expected (present value) returns and cash outlays for the projects are given below. Fox can undertake any of the projects partially or completely. A partial undertaking of a project will prorate both the return and cash outlays proportionately.

Cash outlay ($1000)

Project Year 1 Year 2 Year] Year 4 Return ($1000)

1 10.5 14.4 2.2 2.4 32.40 2 8.3 12.6 9.5 3.1 35.80 3 10.2 14.2 5.6 4.2 17.75 4 7.2 10.5 7.5 5.0 14.80 5 12.3 10.1 8.3 6.3 18.20 6 9.2 7.8 6.9 5.1 12.35 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. 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 undertaken. Modify the formulation of the model and find the new optimal solution.