$6\mathrm{.}1.$ Reconsider the Super Grain Corp. case study as preserted in Section $6\mathrm{.}1.$ The advertising firm, Giacomi & Jackowit, now has suggested a fourth promising advertising medium$-$radio commercials$-$to promote the company's new breaklast cereal, Crunchy Start. Young children are potentially major consumers of this cereal, but parents of young children $($the major potential purchasers$)$ often are too busy to do much reading $($so may miss the company's advertisements in Sunday supplements$)$ or even to watch the Saturday morning programs for children where the company's television commercials are aired. However, these parents do tend to listen to the radio during the commute to and from work. Therefore, to better reach these parents, Giacomi & Jackowitz suggests giving consideration to running commercials for Crunchy Start on nationally syndicated radio programs that appeal to young adults during typical commuting hours.

Glacomi & Jackowitz estimates that the cost of developing each new radio commertial would be SS$10\mathrm{.}000,$ and that the expected number of exposures per commercial would be $900\mathrm{.}000).$ The firm has determined that il spots are avallable for different radio conmercials, and cach one would cost $$200,000$ for a normal run.

a$.$ Formulate and solve a spreadsheet model for the revised advertising$-$mix problem that includes this tourth advertising mediun. Identify the data cells, the changing cells, and the objective cell Ako show the Excel equation for each ouput cell expressed as a SUMPRODUCT function.

b$.$ Indicalle why this spreadheet model is a linear programming model.

Exprese this model in aleebraic termi.