1. The IRS has determined that during each of the next six months it will need the number of supercomputers given in the table below. To meet these requirements, the IRS rents supercomputers for a period of one, two, or three months. It costs $100 to rent a supercomputer for one month, $180 for two months, and $250 for three months. At the beginning of month 1, the IRS has no supercomputers. Determine the rental plan that meets the requirements at minimum cost. Note: You may assume that fractional rentals are okay. Use the Simplex (or Two Phase Simplex) method. You can implement this method in Excel but I am not asking you to use Excel's solver.
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Month
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1
|
2
|
3
|
4
|
|
Computer requirements
|
800
|
600
|
500
|
600
|
2. Carco has a $150,000 advertising budget. To increase automobile sales, the firm is considering advertising in newspapers and on television. The more Carco uses a particular medium, the less effective is each additional ad. The table below shows the number of new customers reached by each ad. Each newspaper ad costs $1,000, and each television ad costs $9,000. At most, 30 newspaper ads and 15 television ads can be placed. How can Carco maximize the number of new customers created by advertising? First formulate the problem then solve it with Excel's solver!
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Student
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Number of Ads
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New Customers
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Newspaper
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1-10
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900
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11-20
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600
|
|
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21-30
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300
|
|
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Television
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1-5
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10,000
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6-10
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5,000
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|
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11-15
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2,000
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|
3. Consider the following LP:
max z = 10x1 + x2
s.t. x1 ≤1
20x1+ x2≤ 100
x1,x2≥ 0
a. Find all the basic feasible solutions (bfs) for this LP. (Hint: consider all possible combinations of basic variables)
b. Show that when the simplex algorithm is used to solve this LP, every bfs will be examined before the optimal is found.
4. Use the simplex algorithm to solve the following LP:
max z = 2x1 + x2
s.t. x1+ x2≤ 4
3x1+ x2≤ 6
x1≥ 0,x2 urs.