Question

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 ($)
Alternative Net Present Value ($) Year 1 Year 2 Year 3
Limited warehouse expansion 4,000 3,000 1,000 4,000
Extensive warehouse expansion 6,000 2,500 3,500 3,500
Test market new product 10,500 6,000 4,000 5,000
Advertising campaign 4,000 2,000 1,500 1,800
Basic research 8,000 5,000 1,000 4,000
Purchase new equipment 3,000 1,000 500 900
Capital funds available 10,500 7,000 8,750

Develop an integer programming model for maximizing the net present value.

Answer 1

Answer:

Assume: only one of the ware house expansion projects can be implemented and suppose that, if test marketing of the new product is carried out, the advertising campaign also must be conducted and vice versa. Also suppose that the purchase of new equipment cannot be undertaken unless the basic research or the extensive warehouse expansion are implemented.

Formulate the corresponding model for maximizing the net present value subject to the restrictions stated above

Yi (1 if investment alternative is selected, o otherwise)

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

Max Z = $4,000y1 + 6,000y2 + 10,500y3 + 4,000y4 + 8,000y5 + 3,000y6

∴ NPV = 17,500