# Quantitative methods

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Assignment Problem 1*
Print Media Advertising (PMA) has been given a contract to market Buzz Cola via newspaper ads in a major southern newspaper. Full-page ads in the weekday editions (Monday through Saturday) cost \$2000, whereas on Sunday a full-page ad costs \$8000. Daily circulation of newspaper is 30,000 on weekdays and 80,000 on Sundays.
PMA has been given a \$40,000 advertising budget for the month of August. The experienced advertising executives at PMA 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 fractional 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 half-page ad. Also, assume that smaller ads reduce exposure and costs proportionately.) This August has 26 weekdays and 5 Sundays.
The objective is to determine the optimal placement of ads by PMA in the newspaper during August so as to maximize the cumulative total exposure (as measured by circulation) for the month of August.
a) Formulate the linear programming model for the problem.
b) Use the Graphical method to find the optimal solution. Show all steps.
c) Use Excel Solver to find the optimal solution. Copy and paste your spreadsheet and the Answer report in its entirety from Excel. Remember to not delete/modify any part of the Answer Report.

• Quantitative methods -

w = # of workday ads
s = # of sunday ads

cost constraint
2,000 w + 8,000 s </= 40,000
or simplified
w + 4 s </= 20

days needed constraints
8 </= w </= 26
2 </= s </= 5

graph these, box for the two days needed with line sloping down from left through the box for cost
three intersections
(2,8) , (2,12) , (3,8)

maximize E = 30,000 w + 80,000 s
check those three corners and pick the one with the biggest E