Giacomi & Jackowitz estimates that the cost of developing each new radio commercial would be $$50,000,$ and that the expected number of exposures per commercial would be $900,000.$ The firm has determined that $10$ spots are available for different radio commercials, and each one would cost $$200,000$ for a normal run.

a$.$ Formulate and solve a spreadsheet model for the revised advertising$-$mix problem that includes this fourth advertising medium. Identify the data cells, the changing cells, and the objective cell. Also show the Ex'cel equation for each output cell expressed as a SUMPRODUCT function.

b$.$ Indicate why this spreadsheet model is a linear programming model.

c$.$ Express this model in algebraic form.