Reference no: EM132253633
A company is hired to promote a new smartphone product wants to get the best exposure possible for the product and stay within its budget of $120,000 during the next financial quarter. To do so, the firm 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 Sunday Newspaper. Each television spot costs $4000; each Sunday newspaper ad costs $1000. The expected exposure, based on industry ratings, is 30,000 viewers for each television commercial and 20,000 readers for each newspaper advertisement. The firm’s Director knows from experience that it is important to use both types of media in order to reach the broadest spectrum of potential customers. She decides that at least 10 but no more than 25 television spots should be ordered and that the number of newspaper ads should be no more than 4 times the number of television spots. How many times should each of the two media be used in the next financial quarter to obtain maximum exposure while staying within its client’s budget?
a) Formulate the problem into “Proper LP format” and solve graphically using ONLY Isoprofit lines (level curves) (do not solve by evaluating all the extreme corners of the feasible area). Make sure to plot the Television spots along the horizontal axis of your graph paper. Clearly state the optimal solution in terms of the business problem. Be sure to state the value of the objective function with respect to the optimal solution.
b) Using your answer in part a) solve algebraically for the two constraints involved in the optimal solution.
c) Suppose the firm’s client is willing to increase its budget for advertising beyond the $120,000 budget in the next financial quarter. Should it do so? State why or why not. How much more should they consider increasing it? (providing that all other constraints remain the same)
d) Suppose a new industry report has been released stating that expected exposure is 90,000 viewers for each television commercial and 20,000 readers for each newspaper advertisement. Assuming this to be true, state the new objective function. Using the original problem constraints, plot the new objective function on your existing graph and determine if a new optimal solution exists or not. State the exact coordinates if a new optimal solution exists (ie check algebraically). Clearly state the optimal solution in the context of the business problem if there is a new optimal solution.
e) The firm’s Director is considering removing the maximum number of television spots, currently set at a maximum of 25, in order to increase exposure. Using your graphical solution defined in part d), should the firm do so? State why or why not. How much more should they consider increasing it to? (providing that all other constraints remain the same)