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Example 6 Video Example the store offer to maximize its revenue? A store has been selling 500 TV monitors a week at $550 each. A market survey indicates that for each $30 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 Solution If x 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 $30. So for each additional unit said, the decrease in price will be * 30 and the demand function is p(x) - 550 - (x - 500) = BOD - The revenue function is R(x) = xp (x) = Since R'(x) . we see that R'(x) = 0 when x= . This value of x gives an absolute maximum by the First Derivative Test (or simply by observing that the graph of R is a parabola that opens downward). The corresponding price is p(800) and the rebate is 550 - 400 - Therefore, to maximize revenue, the store should offer a rehate of $ Need Help? Read It