A business is currently selling 30 chairs per day for a price of $25 p

Solution:

Let x be the number of dollars the price of a chair is lowered from $25 (notice that x is also the number of more chairs that can be sold beyond 30). Since revenue = quantity * unit price and if we let y be the revenue, we have:

y = (30 + x)(25 - x)

y = 750 - 5x - x^2

y = -x^2 - 5x + 750

Notice the equation above is a quadratic equation whose graph is a downward parabola. So the maximum revenue is the y-coordinate of the vertex. For a quadratic equation of the form y = ax^2 + bx + c (where a ≠ 0), the maximum value occurs when x = -b/(2a). Since here, a = -1 and b = -5, the maximum value occurs when x = -(-5)/(2 * -1) = -2.5. Since x is negative and we only concern ourselves with the values of y where x is nonnegative, it means the maximum value of y occurs at x = 0. Therefore, the maximum revenue is y = (30 + 0)(25 - 0) = 30 * 25 = $750. (In other words, do not lower the price. For example, if you lower the price by $1 to $24, the number of chairs sold increases by 1 to 31. However, the revenue will then be 31 x 24 = $744, which is lower than $750.)

Answer: D