Question

The profit function of producing x units in P(x)=-0.025x^2+9.85x-60, maximum loss is

Answer 1

To find the maximum loss, we need to determine the minimum value of the profit function P(x).

To find the minimum value, we can use the formula for the x-coordinate of the vertex of a quadratic function: x = -b / (2a), where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.

In this case, the quadratic function is P(x) = -0.025x^2 + 9.85x - 60. Comparing this to the general form ax^2 + bx + c = 0, we can see that a = -0.025, b = 9.85, and c = -60.

Now we can substitute these values into the formula: x = -9.85 / (2*(-0.025)).

Simplifying this expression gives: x = -9.85 / (-0.05) = 197.

Therefore, the x-coordinate of the vertex of the profit function is x = 197.

To find the minimum value of the profit function, we substitute this x-coordinate into the function: P(197) = -0.025(197)^2 + 9.85(197) - 60.

Calculating this expression gives: P(197) = -972.5 + 1936.45 - 60 = 903.95.

Hence, the maximum loss is $903.95.