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	3,500	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	8,500	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

An integer programming model for maximizing the net present value (in $) is developed.

Letting x_i =

1 if investment alternative i is selected

0 otherwise

for i = 1, 2, 3, 4, 5, 6.

(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?