Print Media Incorporated Advertising (PMIA) has been given a contract to market

Question

Print Media Incorporated Advertising (PMIA) has been given a contract to market chill Cola via newspaper ads in a major Northern newspaper. Full-page ads in the weekday editions (Monday through Saturday) cost $2000 per day, whereas on Sunday a full-page ad costs $8000. Daily circulation of the newspaper is 30,000 on weekdays and 80,000 on Sunday.
PMIA has been given a $40,000 advertising budget for the month of August. The experienced advertising executives at PMIA feel that both weekday and Sunday newspaper ads are important; hence, they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fraction of ad would simply mean that a smaller ad is placed on one of the days; that is, 3.5 ads would mean three full-page ads and one one-half page ad. Also assume that smaller ads reduce exposure and cost proportionately.) This August has 26 weekdays and 5 Sundays.
If the objective is to maximize cumulative total exposure (as measured by circulation) for the month of August, answer the following questions:
a)Write the linear programming model for this problem. Define the variables precisely. (Hint: PMA is deciding how to advertise in a major newspaper.)
b) Find the optimal solution using the graphical method. Show all steps. Find the points of intersection algebraically.
c) Find the optimal solution using Excel Solver. Copy and paste the Excel spreadsheet and the Answer Report

Explanation / Answer

(a) Linear Programming model: Define Variables: Wf=Weekday full page ads Sf=Sunday full page ads Objective is: Maximize Advertisement exposure Z=26Wf+5Sf Constraints: Number of days: 8Wf+2Sf=31 (1) Cost of Ads: 2000Wf+8000Sf=40000 (2) Size of Ads: Wf+Sf=3.5 (3) Non-negativity: Wf=0 and Sf=0

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