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 combination of commercial and advertisements that would maximize the exposure would be$,$ respectively:

Integer Programming: $x_1=8$;$x_2=1$;$x_3=6$;

Linear Programming: $x_1=8$;$x_2=1\mathrm{.}71$;$x_3=6$;

Integer Programming: $x_1=6$;$x_2=4$;$x_3=5$;

Linear Programming: $x_1=6$;$x_2=4\mathrm{.}57$;$x_3=5$;

Integer Programming: $x_1=6$;$x_2=5$;$x_3=6$;

Linear Programming: $x_1=6$;$x_2=4\mathrm{.}57$;$x_3=5$;

Integer Programming: $x_1=6$;$x_2=2$;$x_3=8$;