A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided estimates of the audience exposure for each minute of advertising in each medium, which it would like to maximize. Costs per minute of advertising are also known, and the manager has a limited budget of $$25,000.$ The manager has decided that because television ads have been found to be much more effective than radio ads, at least $70\%$ of the time should be allocated to television. Data is provided.

How much time in minutes for TV should be allocated?

Round to $2$ decimals

Hint:

You can linearize the constraint that involves proportion.

For example,

A & B where B must be greater than or equal to $60\%$ total $($A$+$B$)$

B $>=0\mathrm{.}6$T

B $>=0\mathrm{.}6($A $+$B$)$

B $>=0\mathrm{.}6$A $+0\mathrm{.}6$B

$-0\mathrm{.}6$A $+0\mathrm{.}4$B $>=0$

Type of Ad Unit Exposure $/$ Minute Cost $/$ Minute Budget Limit: $$25,000$

Radio $350$ $$400$ Tv ad requirement at least $70\%$ of total time

TV $800$ $$2,000$