Question

The graph of the function P(x) = −0.52x2 + 23x + 92 is shown. The function models the profits, P, in thousands of dollars for a candle company to manufacture a candle, where x is the number of candles produced, in thousands: graph of a parabola opening down passing through points negative 3 and 69 hundredths comma zero, zero comma 92, 6 and 84 hundredths comma 225, 22 and 11 hundredths comma 346 and 33 hundredths, 37 and 39 hundredths comma 225, and 47 and 92 hundredths comma zero If the company wants to keep its profits at or above $225,000, then which constraint is reasonable for the model? 0 ≤ x < 6.84 and 37.39 < x ≤ 47.92 −3.69 ≤ x ≤ 6.84 and 37.39 < x ≤ 47.92 6.84 ≤ x ≤ 37.39 −3.69 ≤ x ≤ 47.92

Answer 1

6.84 ≤ x ≤ 37.39

Explanation:

we have

`P(x)=-0.5x^2+23x+92` -----> equation A

we know that

The company wants to keep its profits at or above $225,000,

so

`PXx)\geq 225` -----> inequality B

Remember that P(x) is in thousands of dollars

Solve the system by graphing

using a graphing tool

The solution is the interval [6.78,39.22]

see the attached figure

therefore

A reasonable constraint for the model is

6.84 ≤ x ≤ 37.39