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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.

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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.

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