Question

The graph of the function P(x) = −0.34x2 + 12x + 62 is shown. The function models the profits, P, in thousands of dollars for a tire company, where x is the number of tires produced, in thousands: graph of a parabola opening down passing through points negative 4 and 57 hundredths comma zero, zero comma 62, 1 and 12 hundredths comma 75, 17 and 65 hundredths comma 167 and 55 hundredths, 34 and 18 hundredths comma 75, and 39 and 87 hundredths comma zero If the company wants to keep its profits at or above $75,000, then which constraint is reasonable for the model?

Answer 1

1.119 ≤ x ≤ 34.175

Explanation:

In the picture attached, the plot of P(x) = −0.34x2 + 12x + 62 is shown, where P is the profits. X represents the number of tires produced, so it must be positive.

From the picture, we can see that the values of P(x) greater-than-or-equal-to $75,000 correspond to the values of x between 1.119 and 34.175.