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. At most one of the warehouse expansion alternatives can be chosen.

			Capital Requirements ($)
Alternative Number	Alternative	Net Present Value ($)	Year 1	Year 2	Year 3
1	Limited warehouse expansion	4,500	1,000	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	3,500	1,000	500	900
	Capital funds available		9,000	11,000	12,000

(a)

Develop an integer programming model for maximizing the net present value (in $). (Let x_i = 1 if investment alternative i is selected, 0 otherwise, for i = 1, 2, 3, 4, 5, 6.)

Max ______

s.t.

Year 1 ______

Year 2 ______

Year 3 ______

warehouse expansions ______

x_i = 0, 1 for i = 1, 2, 3, 4, 5, 6

According to this model, what is the maximum net present value (in $)?

$______

(b)

Suppose that if the Advertising campaign is chosen, then the Test market new product alternative must be chosen. Modify your model from part (a) to take this into account.

In addition to the constraints from part (a), what additional constraint should be added to the integer programming model?

_______

According to this model, what is the maximum net present value (in $)?

$______

(c)

Suppose the Extensive warehouse expansion must be chosen. Modify your formulation from part (b) to reflect this new situation.

In addition to the constraints from part (a) and part (b), what additional constraint should be added to the integer programming model?

_______

According to this model, what is the maximum net present value (in $)?

$______

What is the impact of this constraint on the optimal NPV in comparison to the optimal NPV from part (b)?

Compared to the optimal NPV from part (b), the optimal NPV decreased with the additional constraint.

			Capital Requirements ($)
Alternative Number	Alternative	Net Present Value ($)	Year 1	Year 2	Year 3
1	Limited warehouse expansion	4,500	1,000	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	3,500	1,000	500	900
	Capital funds available		9,000	11,000	12,000