a. Develop and solve an integer programming model for maximizing the net present value. b. Assume that only one of the warehouse expansion projects can be implemented. Modify your model from part (a). c. Suppose that if test marketing of the new product is carried out, the advertising campaign also must be conducted. Modify your formulation from part (b) to reflect this new situation.

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1. Investment Net Present Value. 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 (5)
Alternative
Limited warehouse
expansion
Extensive warehouse
expansion
Test market new
product
Advertising campaign
Basic research
Purchase new
equipment
Capital funds available
Net Present
Value (5)
4,000
6,000
10,500
4,000
8,000
3,000
Year 1
3,000 1,000
Year 2
2,500 3,500
1,000
Year 3
6,000 4,000 5,000
10,500
4.000
2,000 1,500 1,800
3,500
5,000 1,000 4,000
500
900
7,000 8,750
a. Develop and solve an integer programming model for maximizing the net present value.
b. Assume that only one of the warehouse expansion projects can be implemented. Modify your
model from part (a).
c. Suppose that if test marketing of the new product is carried out, the advertising campaign
also must be conducted. Modify your formulation from part (b) to reflect this new situation.
2. Machine Tool Production Planning. King City Inc. manufactures machine tools. The production
planner who oversees the production of two of King City's machines needs to determine how
many of each to produce this month. The two machines, TopLathe and BigPress, each require a
certain common component. Each TopLathe requires 10 of these components and each BigPress
requires 7. Only 49 components are available this month. The sales department requires that
the total number of machines produced in a month must be at least 5 (the number TopLathes
plus the number BigPresses must be at least 5). The profit for a TopLathe is $50,000 and $34,000
for a BigPress.
a. Assuming that adequate labor and all other resources are available, formulate an integer
programming model to determine how many of each product King City should produce to
maximize profit.
b. Based on the solution for the LP relaxation model given below, round the TopLathe and
BigPress values. Is the solution feasible? Why?
Transcribed Image Text:1. Investment Net Present Value. 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 (5) Alternative Limited warehouse expansion Extensive warehouse expansion Test market new product Advertising campaign Basic research Purchase new equipment Capital funds available Net Present Value (5) 4,000 6,000 10,500 4,000 8,000 3,000 Year 1 3,000 1,000 Year 2 2,500 3,500 1,000 Year 3 6,000 4,000 5,000 10,500 4.000 2,000 1,500 1,800 3,500 5,000 1,000 4,000 500 900 7,000 8,750 a. Develop and solve an integer programming model for maximizing the net present value. b. Assume that only one of the warehouse expansion projects can be implemented. Modify your model from part (a). c. Suppose that if test marketing of the new product is carried out, the advertising campaign also must be conducted. Modify your formulation from part (b) to reflect this new situation. 2. Machine Tool Production Planning. King City Inc. manufactures machine tools. The production planner who oversees the production of two of King City's machines needs to determine how many of each to produce this month. The two machines, TopLathe and BigPress, each require a certain common component. Each TopLathe requires 10 of these components and each BigPress requires 7. Only 49 components are available this month. The sales department requires that the total number of machines produced in a month must be at least 5 (the number TopLathes plus the number BigPresses must be at least 5). The profit for a TopLathe is $50,000 and $34,000 for a BigPress. a. Assuming that adequate labor and all other resources are available, formulate an integer programming model to determine how many of each product King City should produce to maximize profit. b. Based on the solution for the LP relaxation model given below, round the TopLathe and BigPress values. Is the solution feasible? Why?
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