6.Todetermine the number of ads, you will need to graph theintersectionof all fiveinequalities on one common XY plane(Do not plot the objective function!).Use Desmos.com to plot the inequalities. Scale your axes (or zoom in) so that you have the bottom left be the origin, with the horizontal axis representing X and the vertical axis representing Y. Include your graph with your assignment by either taking a screen shot of it or using the print feature on Desmos. Label the points of intersection on your graph as well. 7.Theshaded region in theabovegraphis called thefeasible region. Any (x, y) point in the region corresponds toa possible number ofradio and TV ads that will meetall the requirements of the problem. However, the values that willmaximizethenumber of people exposed to the ads willoccur at one of the vertices or corners of the region. Your regionshould havethreecorners.

Find the coordinatesofthese cornersby solving theappropriate systemsof linear equations. Be sure toshow your workandlabelthe (x, y) coordinates of the corners in your graph.

8.To find whichcombinationof radio and TV adswill maximize thenumber of people who are exposed to thebusinessadvertisements,evaluate the objective function P for each of the vertices you found.Show your work.

i.Vertex:

ii.Vertex:

iii.Vertex:

9.Write a sentenceor twodescribingyour conclusion.Include in your statement:how many of each type ofadvertisementshouldbe purchasedand what isthe maximum number of people who will be exposed to the ads.

10.Reflective Writing.

This needs to be a separate page that is typed, proof-read for typos, spelling, and grammar. Your writing should be in an essay form (written in paragraphs). Use 12-point font and double space. Add a title (e.g. Reflective Writing forOptimizationProject). Your instructor will provide details for turning it in. Provide a brief introduction explaining the lab in your own words.Alsoin the introduction, tell the audience which mathematical techniques you used in the lab (e.g.linear equations,etc.). Then, please respond to each of the questions (in essay form, soparaphrasethe question you are answering).

Can you give an example of another application where this type of analysis would be beneficial? Be specific.If you worked foran advertising agency, why would it be important to be able to explain the details of this project to clients?Discuss in your own words how the results might change if the given information (i.e. numbers of ads, costs, budget) changed. How would you interpret a result if the vertices weren't at integer values? For example, what if you found 15.2 radio ads and 46.8 TV ads? What would you do?Did this assignment change your opinion of the usefulness of math? Write one paragraph stating what ideas changed and why. If this project did not change the way you think, write how this project gave further evidence to support your existing opinion about applying math. Be specific.