Please formulate the problem below, solve it on the QM software, print the outpu
ID: 3232157 • Letter: P
Question
Please formulate the problem below, solve it on the QM software, print the output, interpret the results as instructed below, then bring the printout along with the interpretation to the exam. Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7, 200 per week. The total number of ads should be at least 15, with at least 2 of each type. Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people. The company wishes to reach as many people as possible while meeting all the constraints stated. Formulate as an LP Solve using QM or any software of your choice, then interpret your output (the optimal solution, the reduced costs, slack/surplus, dual prices, ranges of feasibility, ranges of optimality)Explanation / Answer
Lets say total Radio ads = X and total Newspaper ads = Y
COst of radio ads = $ 400 and Cost of newspaper ads = $ 600
Total Budget= 400X + 600Y
Total viewership of Radio Ads = 2000
Total viewership of Newsapaper Ads = 6000
So we have to maximize the viewership
so Maximum Viewership = 2000X + 6000Y
with constraint
400X + 600Y <= 7200...(i)
X + Y >= 15....(ii)
X >= 2
Y >= 2
I am solving this problem by excel solver and presenting here the summary , ANswer and sensitivity report.
Here Ansswer Report
So number of Radio Ads = 9
Number of Television ads = 6
Total maximum viewership = 9 * 2000 + 6 * 6000 = $54000
Target Cell (Max) Cell Name Original Value Final Value $E$4 Viewership Maximize 0 54000 Adjustable Cells Cell Name Original Value Final Value $C$3 Number of ads Radio 0 9 $D$3 Number of ads TV 0 6 Constraints Cell Name Cell Value Formula Status Slack $E$6 Cost Maximize 7200 $E$6<=7200 Binding 0 $E$7 Total Ads Maximize 15 $E$7>=15 Binding 0 $C$3 Number of ads Radio 9 $C$3>=2 Not Binding 7 $D$3 Number of ads TV 6 $D$3>=2 Not Binding 4