The Biggs Department Store chain has hired an advertising firm to determine the types and amount of advertising it should invest in for its stores. The three types of advertising available are television and radio commercials and newspaper ads. The retail chain desires to know the number of each type of advertisement it should purchase in order to maximize exposure. It is estimated that each ad or commercial will reach the following potential audience and cost the following amount:

Exposure

$($people$/$ad or commercial$)$

Cost $($US$$)$

TV commercial

$40,000$

$16,000$

Radio commercial

$28,000$

$14,000$

Newspaper ad

$29,000$

$8,000$

The company must consider the following resource constraints:

The budget limit for advertising is $$200,000.$

The television station has time available for $6$ commercials.

The radio station has time available for $12$ commercials.

The newspaper has space available for $5$ ads.

The advertising agency has time and staff available for producing no more than a total of $20$ commercials and$/$or ads.

If this problem is formulated as an integer and also a linear programming problem $($separately$),$ the maximization $("$Z$",$ the optimal solution$)$ of the exposure would be$,$ respectively:

Group of answer choices

Integer Programming: $497,000$ ;

Linear Programming: $513,000$ ;

Integer Programming: $457,000$ ;

Linear Programming: $497,000$ ;

Integer Programming: $513,000$ ;

Linear Programming: $457,000$ ;

Integer Programming: $497,000$ ;

Linear Programming: $457,000$ ;

None of the above