(Advertising problem) 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
I know that this a minimisation linear programing, and the variables for the problem are TV and Radio, but how do I set up the inequalities?
EDIT: it seems that what I assumed to be minimising cost is actually a maximisation problem
Best Answer
Let $T$ be the number of TV advertising minutes per month, and $R$ the number of radio advertising minutes per month.
The constraints are (1) $300T+15R\le10000$ (limited budget), (2) $R\ge 2T$, (3) $R\le 400$, (4) $T\ge 0$.
Note that we do not need $R\ge 0$ because it follows from (2) and (4).
We want to maximise $R+25T$ which is a measure of effectiveness.