Linear Programming

1. Advertising Mix

A company has a weekly advertising budget of $80,000 to allocate over four different media in a particular market:  TV spots, newspaper ads, and two types of radio advertisement.  The cost, reach, and limits to each type of advertising is given in the table below:

The company wants to reach as many people as possible with its advertising.  To ensure a broad-scoped promotional campaign, the company limits spending on radio advertising to no more than $18,000 per week.  Also, in order to saturate the afternoon with broadcast media, at least 40 percent of the radio ads have to be in the afternoon.

a. What is the optimal distribution of the company's advertising budget?  Give the number of ads bought in each media and the amount spent on each media.

b. How many people will the company reach with its ads?

c. Does the company have any excess money left?

2. Employee Scheduling

A restaurant wants to schedule its employees in the most efficient (least costly) way. It has determined that it needs the following number of workers at different times of the day:

In addition to having enough people at the different times of the day, the restaurant also needs to meet the following requirements:

• At least two full-time employees must be on duty when the restaurant opens at 6 AM
  
  
• At least two full-time employees must be on duty when the restaurant closes at 10 PM
  
  
• At least four full-time employees must be on duty during the lunch period (12 PM - 2 PM).
  
  
• At least six full-time employees must be on duty during the dinner period (6 PM - 8 PM).

The restaurant operates with seven different shifts:

a. How many workers should be hired for each shift?

b. What is the restaurants total wage bill?

c. What periods, if any, have excess (slack) employees, and how much is that excess?

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3. Transportation

Suppose the table below shows the travel costs between two of Amazon's distribution centers (D1, D2) and four of its markets (M1, M2, M3, M4):

D1 has 40 units of a particular product while D2 has 45 units. The demands in the four markets are 20, 16, (f), and (g), respectively.

a. How much should Amazon send from each distribution center to each of the markets?

b. What is the total transportation cost?

c. Give an interpretation of each calculated shadow price in this situation.

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Final Output

Please submit a copy of your analysis along with supporting computer output by Thursday, April 23. If the output is a hard copy, it should be typed on 8 ½ x 11 or A4 paper. Please do not submit the report in a special report cover; a stable in the upper left hand corner would be adequate.  The output may also be submitted as an e-mail attachment.