Question

Question
A company's revenue from selling `p` phone cases is modeled by R(p)=−4p2+120p
. According to the provided graph, how many phone cases must be sold to generate a revenue of $800 for the first time?

Graph showing phone case sales revenue analysis with a curve and data points.
(1 point)
Responses

25 phone cases
25 phone cases

15 phone cases
15 phone cases

10 phone cases
10 phone cases

20 phone cases
20 phone cases
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Answer 1

Set R(p) = 800: -4p^2 + 120p = 800 → -4p^2 + 120p - 800 = 0 → p^2 - 30p + 200 = 0.
Solve: p = [30 ± √(900 − 800)]/2 = [30 ± 10]/2 → p = 10 or 20.
The revenue reaches $800 for the first time at 10 phone cases.