Question

A company sells sweaters. The amount of profit, y, made by the company is related to the selling price of each sweater, x, by the given equation. Using this equation, find out what price the sweater should be sold for, to the nearest cent, for the company to make the maximum profit.

Y = -9x^2 + 700x - 6005

Answer 1

To maximize profit described by the quadratic equation Y = -9x² + 700x - 6005, one should calculate the vertex of the parabola. Using the vertex formula, the optimal selling price of the sweater is $38.89 to the nearest cent.

Step-by-step explanation:

The equation Y = -9x² + 700x - 6005 represents a quadratic equation, where 'y' is the profit and 'x' is the selling price per sweater. To maximize profit (y), we need to find the vertex of the parabola this equation represents, because the vertex will give us the maximum or minimum point, and since the coefficient of x² is negative, this parabola opens downwards, indicating a maximum.

The vertex formula for a parabola y = ax² + bx + c is given by x = -b/(2a). Applying this formula to the given equation, we would have:

x = -700/(2×(-9))x = -700/(-18)x = 38.89

To the nearest cent, the company should sell each sweater for $38.89 to achieve the maximum profit.