W$1-3.($Media Selection$)$ The advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $$100,000$ advertising budget ceiling placed upon it$.$ To do so$,$ the agency needs to decide how much of the budget to spend on each of its two most effective media: $(1)$ television spots during the afternoon hours and $(2)$ large ads in the city's Sunday newspaper. Each television spot costs $$3,000$; each Sunday newspaper ad costs $$1,250.$ The expected exposure, based on industry ratings, is $35,000$ viewers for each TV commercial and $20,000$ readers for each newspaper advertisement. The agency director, Mavis Early, knows from experience that it is important to use both media in order to reach the broadest spectrum of potential Breem customers. She decides that at least $5$ but no more than $25$ television spots should be ordered; and that at least $10$ newspaper ads should be contracted. How many times should each of the two media be used to obtain maximum exposure while staying within the budget? Use linear programming to solve.

$($Source: Quantitative Analysis for Management $(7$th Ed$.),$ Render, Stair, & Hana. Pearson$).$

Task One:

Solve below:

$1.$ Model the problem as a LP problem.

$2.$ Use POM$-$QM to solve the problem using the corner points method.

$3.$ Provide the managerial interpretation.

Task Two:

Write the case study:

$1.$ Introduction to the case study

$2.$ Purpose of the study

$3.$ Formulation of the LP problem

$4.$ The LP problem setup in the software

$5.$ The outputs generated by the software

$6.$ Managerial interpretation of the results

$7.$ Your recommendations for solving the case study