Marketing managers have various media alternatives, such as radio, tv, magazines etc. in which to advertise and must determine which to use, the number of insertions in each and the timing of insertions to maximise advertising effectiveness within a limited budget. Suppose that three media options are available to Kernan Services Corporation: radio, tv and magazine. The following table provides some information about costs, exposure values, and bounds on the permissible number of ads in each medium desired by the firm. The exposure value is a measure of the number of people exposed to the advertisement and is derived from market research studies, and the client's objective is to maximise the total exposure value. The company would like to achieve a total exposure value of at least 90,000

Medium cost/ad Exposure value/ad Min units Max units
Radio $500 2000 0 15
TV $2000 4000 10
magazine $200 2700 6 12

How many of each type of ad should be placed in order to minimise the cost of achieving the minimum required total exposure. Use the auxiliary variable approach to model this problem and write a short memo to the marketing manager explaining the solution and sensitivity information.