The graph of the function P(x) = −0.74^2 + 22x + 75 is shown. The function models the profits, P, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands: If the company wants to keep its profits at or above $175,000, then which constraint is reasonable for the model? −3.09 ≤ x ≤ 5.6 and 24.13 < x ≤ 32.82 0 ≤ x < 5.6 and 24.13 < x ≤ 32.82 −3.09 ≤ x ≤ 32.82 5.6 ≤ x ≤ 24.13

5.6 ≤ x ≤ 24.13.

Step-by-step explanation:

Given, The graph of the function . The function models the profits, P, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

In graph , On axis → number of calculators produced

On y-axis →  profit made in thousands of dollars.

From the graph, the curve goes for y > 175 from x = 5.6 to x= 24.13 ( approx)

So, the reasonable constraints for the model 5.6 ≤ x ≤ 24.13.

So, If the company wants to keep its profits at or above $175,000, reasonable constraints for the model 5.6 ≤ x ≤ 24.13.