A store has been selling $400$ TV monitors a week at $\backslash (\backslash$$ $450\backslash )$ each. A market survey indicates that for each $\backslash (\backslash$$ $30\backslash )$ rebate offered to buyers, the number of monitors sold will increase by $60$ a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue? Solution If $\backslash ($ x $\backslash )$ is the number of monitors sold per week, then the weekly increase in sales is $.$ For each increase of $60$ units sold, the price is decreased by $\backslash (\backslash$$ $30\backslash ).$ So for each additional unit sold, the decrease in price will be $\backslash (\backslash$frac$\{1\}\{60\}\backslash$times $30\backslash )$ and the demand function is