[SOLVED] An integer programming model..

[SOLVED] An integer programming model..

10- 17 A real estate developer is considering three possible projects: a small apartment complex, a small shopping center, and a mini-warehouse. Each of these requires different funding over the next 2 years, and the net present values of the investments also vary. The following table provides the required investment amounts (in $1,000s) and the net present value (NPV) of each (also expressed in $1,000s):

INVESTMENT
NPV YEAR 1 YEAR 2
Apartment complex 18 40 30
Shopping center 15 30 20
Mini-warehouse 14 20 20

The company has $80,000 to invest in year 1 and $50,000 to invest in year 2.
Develop an integer programming model to maximize the NPV in this situation.
Solve the problem in part (a) using computer software. Which of the three projects would be undertaken if NPV is maximized? How much money would be used each year?

 

10-20 The campaign manager for a politician who is running for reelection to a political office is planning the campaign. Four ways to advertise have been selected: TV ads, radio ads, billboards, and social media advertising buys. The costs of these are $900 for each TV ad, $500 for each radio ad, $600 for a billboard for 1 month, and $180 for each buy on social media (approximately 40,000 unique impressions). The audience reached by each type of advertising has been estimated to be 40,000 for each TV ad, 32,000 for each radio ad, 34,000 for each billboard, and 17,000 for each social media buy. The total monthly advertising budget is $16,000. The following goals have been established and ranked:
The number of people reached should be at least 1,500,000.
The total monthly advertising budget should not be exceeded.
Together, the number of ads on either TV or radio should be at least 6.
No more than 10 ads/buys of any one type should be used.

Formulate this as a goal programming problem.
Solve this using computer software.
Which goals are exactly met and which are not?


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