Problem

Set up the initial simplex tableau that could be used to solve the following problem by the simplex method.
The Fancy Fashions, an independent, local boutique, has $9000 available each month for advertising. Newspaper ads cost $500 each, and no more than 30 can run per month. Internet banner ads cost $20 each, and no more than 60 can run per month. TV ads cost $2000 each, with a maximum of 15 available each month. Approximately 5000 women will see each newspaper ad, 3000 will see each Internet banner, and 11,000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize its ad exposure?

Answer

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Answer

Final Answer: The store should run 16 newspaper ads, 60 internet banner ads, and 0 TV ads to maximize its ad exposure.

Steps

Step 1 :Define the variables: Let x1, x2, and x3 represent the number of newspaper ads, internet banner ads, and TV ads, respectively.

Step 2 :Set up the objective function: The objective function to maximize is 5000x1+3000x2+11000x3, which represents the total number of women who see the ads.

Step 3 :Set up the constraints: The constraints are x130 (no more than 30 newspaper ads), x260 (no more than 60 internet banner ads), x315 (no more than 15 TV ads), and 500x1+20x2+2000x39000 (total cost cannot exceed $9000).

Step 4 :Solve the problem using the simplex method. The optimal solution is x1=15.6, x2=60, and x3=0.

Step 5 :Since the number of ads must be an integer, round x1 down to 16.

Step 6 :Final Answer: The store should run 16 newspaper ads, 60 internet banner ads, and 0 TV ads to maximize its ad exposure.

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