Regional brewer I$-$PA intends to initiate an ad campaign. The client wants to maximize total exposure across all types of advertisements $($TV$,$ Radio, Online, and Mailers$).$ Specifically, the client wants to know how many of each type of ad should be purchased and how many potential customers will be reached after optimizing the marketing mix.$$ Document each step you take to solve the problem, including specification of the linear program. For ease of reporting, provide the optimal number of ads as a decimal without concern for integer programming methods $($e$.$g$.2\mathrm{.}7$ radio ads$).$ The client has decided upon the following requirements for any advertising campaign:

The total advertising budget is $$300,000.$

At least $3$ of each ad type must be purchased.

Radio ads must be more numerous than TV ads. In particular, you are to use at least twice as many radio as TV ads$$

The maximum number of mailers that can be produced is $5$

The maximum number of TV spots available is $4$

The cost and exposure data related to the different types of ads is given below: