The profit function for a certain commodity is

P(x) = 150x − x2 − 1000.
Find the level of production that yields maximum profit, and find the maximum profit.
x =

Incorrect: Your answer is incorrect.
units
P = $

Max profit is the vertex : )

To find the level of production that yields the maximum profit and the maximum profit, we need to find the vertex of the parabola represented by the profit function P(x) = 150x - x^2 - 1000.

The vertex of a parabola can be found using the formula x = -b/2a, where the quadratic equation is in the form ax^2 + bx + c. In this case, a = -1 (since x^2 has a coefficient of -1), b = 150, and c = -1000.

Plugging these values into the formula, we get x = -150 / (2 * -1) = -150 / -2 = 75. The level of production that yields maximum profit is 75 units.

To find the maximum profit, we substitute this value of x back into the profit function, P(x) = 150x - x^2 - 1000:

P(75) = 150 * 75 - 75^2 - 1000 = 11250 - 5625 - 1000 = 4625 dollars.

Therefore, the level of production that yields the maximum profit is 75 units, and the maximum profit is $4625.