The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $$2,000$ between newspaper advertising and radio advertising. Management decided that at least $25\%$ of the budget must be spent on each type of media and that the amount of money spent on local newspaper advertising must be at least one and a half times the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from $0$ to $100,$ with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is $50$ and the value of the index for spot radio advertising is $80,$ how should the restaurant allocate its advertising budget to maximize the value of total audience exposure?

$($a$)$ Formulate a linear programming model that can be used to determine how the restaurant should allocate its advertising budget in order to maximize the value of total audience exposure. If the constant is $"1"$ it must be entered in the box. If your answer is zero enter $"0".$

Let $N=$ amount spent on newspaper advertising

$R=$ amount spent on radio advertising

$($b$)$ Develop a spreadsheet model and solve the problem using Excel Solver. If required, round your answer to two decimal places.

$\backslash$table$[[,$Newspaper,Radio$],[$Dollars Allocated,$$,]]$

Total Exposure Index