The graph of the function p(x) = −0.74x2 + 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:
graph of a parabola opening down passing through points negative 3 and 9 hundredths comma zero, zero comma 75, 5 and 6 tenths comma 175, 14 and 87 hundredths comma 238 and 51 hundredths, 24 and 13 hundredths comma 175, and 32 and 82 hundredths comma zero
if the company wants to keep its profits at or above $175,000, then which constraint is reasonable for the model?
a.)−3.09 ≤ x ≤ 5.6 and 24.13 < x ≤ 32.82
b.)0 ≤ x < 5.6 and 24.13 < x ≤ 32.82
c.)−3.09 ≤ x ≤ 32.82
d.)5.6 ≤ x ≤ 24.13