PromoTime, a local advertising agency, has been hired to promote the new adventure film Tomb Raiders starring Angie Harrison and Joe Lee Ford. The agency has been given a $100,000 budget to spend on advertising for the movie in the week prior to its release, and the movie's producers have dictated that only local television ads and locally targeted Internet ads will be used. Each television ad costs $500 and reaches an estimated 7000 people, and each Internet ad costs $250 and reaches an estimated 4000 people. The movie's producers have also dictated that, in order to avoid saturation, no more than 20 television ads will be placed. The producers have also stipulated that, in order to reach a critical mass, at least 50 Internet ads will be placed. Finally, the producers want at least one-third of all ads to be placed on television. Let

x = the number of television ads purchased
y = the number of Internet ads purchased

a. Develop the objective function, assuming that the movie’s producers want to reach the maximum number of people possible.
b. Show the mathematical expression for the budget constraint.
c. Show the mathematical expression for the maximum number of 20 television ads to be used.
d. Show the mathematical expression for the minimum number of Internet ads to be used.