Question

The weekly revenue from the sale of x units of a product is given by R(x) = 72x - 2x² thousand dollars, where 0 ≤ x ≤ 21. How many units should be sold to maximize the revenue?

Answer 1

To maximize the weekly revenue given by R(x) = 72x - 2x² thousand dollars, one must sell 18 units, as this is the vertex of the parabola represented by the revenue function.

Step-by-step explanation:

The question asks how many units should be sold to maximize the weekly revenue from the sale of a product, given the revenue function R(x) = 72x - 2x² thousand dollars, with the constraint that 0 ≤ x ≤ 21. To find the number of units that maximize revenue, we need to determine the vertex of the parabola represented by the revenue function since it is a downward opening parabola (due to the -2x² term).

To find the vertex, we can use the formula -b/(2a), where a and b are coefficients from the standard form of a quadratic equation ax² + bx + c. In this function, a = -2 and b = 72. Plugging these values into the formula gives us -72/(2 * -2) = 72/4 = 18. Therefore, to maximize revenue, 18 units should be sold.