I apologise as English is not my first language so sometimes I get stuck on problems like these as it can confuse easily.
Show & Sell can advertise its products on local radio and television
(TV). The advertising budget is limited to £10,000 a month. Each
minute of radio advertising costs £15 and each minute of TV
commercials £300. Show & Sell likes to advertise on radio at least
twice as much as on TV. In the meantime, it is not practical to use
more than 400 minutes of radio advertising a month. From past
experience, advertising on TV is estimated to be 25 times as effective
as on radio. Determine the optimum allocation of the budget to radio
and TV advertising. Model this problem as a linear programming
problem.
Here is what I did:
Let $T$ be the number of minutes of TV advertising and $R$ be the number of radio minutes advertising then we have:
Max:$~25R+T\\s.t.\\15R+300T \leq 10000\\2T\leq R\\R \leq 400
\\R,T \geq0$
Is this even near being correct?
Thanks.
Best Answer
It is almost correct. But the objective function has to be $$\texttt{Max} \ \ R+25T$$
The output per one minute advertising on television is 25 times the output per minute advertising on radio.