Before$-$class Activity

Linear Programming

Question $1)$ The Sea Wharf Restaurant would like to determine the best way to plan for its monthly advertising policy and allocate a monthly advertising budget of $$1500$ between newspaper and radio advertising. Each newspaper advertisement costs $$75,$ and each radio advertisement costs $$125.$

Management decided that at least $25\%$ of the budget must be spent on each type of media, and the amount of money spent on local newspaper advertising must be at least twice the amount spent on radio advertising.

A marketing consultant developed an index that measures audience exposure per advertising on a scale from $0$ to $100,$ with higher values implying greater audience exposure. Suppose the value of the index for local newspaper advertising is $40$ and the value of the index for spot radio advertising is $90.$

Let's formulate an LP model that can be used to determine how many newspaper and radio advertisements should be planned to maximize the value of total audience exposure.

Let $,N=$# of newspaper advertisements in each month,

$R=$# of radio advertisements in each month.

b$)$ Write a linear constraint corresponding to the management's concern about spending at least $25\%$ of the budget on each media type.