Question

The graph of the function C(x) = −0.52x2 + 23x + 92 is shown. The function models the production cost, C, 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 production costs under $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
−3.69 ≤ x ≤ 47.92
6.84 ≤ x ≤ 37.39

Answer 1

Answer:

0 ≤ x < 6.84 and 37.39 < x ≤ 47.92

Step-by-step explanation:

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Answer 2

Answer:

0 ≤ x < 6.84 and 37.39 < x ≤ 47.92

Step-by-step explanation:

The costs will be under $225,000 for all x corresponding to points on the graph which are underneath the dotted line.  Of all the proposed answers,

0 ≤ x < 6.84 and 37.39 < x ≤ 47.92 makes sense.  The answer "−3.69 ≤ x ≤ 6.84 and 37.39 < x ≤ 47.92" is tempting, but it includes some negative numbers, and x represents a number of candles!