SALS Marketing Inc. is developing an advertising campaign for a large consumer

goods corporation. SALS has promised a plan that will yield the highest possible $$exposure rating,$$ a

measure of the ability to reach the appropriate demographic group and generate demand. The options

for advertisements with their respective costs $($per unit of advertising$)$ and per$-$unit exposure ratings are

given in the table below.

Category Subcategory Cost$/$Unit Exposure$/$Unit

Magazines Literary $$7,50015000$

News $$10,00022500$

Topical $$15,00024000$

Newspapers Major Evening $$3,00075000$

Major Morning $$2,00037500$

Television Morning $$20,000275000$

Midday $$10,000180000$

Evening $$60,000810000$

Radio Morning $$15,000180000$

Midday $$15,00017000$

Evening $$10,00016000$

Of course, certain restrictions exist for the advertising campaign. The client corporation has budgeted

$$800,000$ for the campaign, but to restrict overexposure to any particular audience it wants no more than

$$300,000$ put into any one category $($Magazine$,$ Newspaper, etc.$).$ Also, to ensure a broad range of

exposure, at least $$100,000$ must be spent in each category.

Formulate the problem as a linear program.

$($a$)$ What are the decision variables?