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

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.