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
1 answer:
Answer:
6.84 ≤ x ≤ 37.39
Step-by-step explanation:
we have
-----> equation A
we know that
The company wants to keep its profits at or above $225,000,
so
-----> 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
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