Spencer Enterprises is attempting to choose among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next three years are summarized as follows. Capital Requirements ($) Alternative Number Alternative Net Present Value ($) Year 1 Year 2 Year 3 1 Limited warehouse expansion 4,500 3,000 1,000 4,000 2 Extensive warehouse expansion 5,500 2,500 3,500 3,500 3 Test market new product 10,000 6,000 4,000 5,000 4 Advertising campaign 4,500 2,000 1,500 1,800 5 Basic research 7,500 5,000 1,000 4,000 6 Purchase new equipment 2,500 1,000 500 900 Capital funds available 10,500 7,000 8,750 / (1 if investment alternative is selected for i = 1, 2, 3, 4, 5, 6.) An integer programming model for maximizing the net present value in $) is developed. Letting x, = i = 2, , 5, 0 otherwise (a) Assume that test market new product will only be funded if the Basic research is also funded. What additional constraint should be added to the integer programming model? (b) Assume if new equipment is purchased, one of the warehouse expansion projects must be implemented. What additional constraint should be added to the integer programming model