A company earns a weekly profit of p dollars by selling x items according to the function p = -x^2 + 125x - 2200. Find the number of items the company must sell each week to obtain the largest possible profit Then find the largest possible profit

Arectemieryf0 2022-07-31 Answered
A company earns a weekly profit of p dollars by selling x items according to the function p = x 2 + 125 x 2200. Find the number of items the company must sell each week to obtain the largest possible profit Then find the largest possible profit.
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Answers (1)

kuglatid4
Answered 2022-08-01 Author has 12 answers
p = x 2 + 125 x 2200 d p d x = 2 x + 125 d p 2 d x 2 = 2
for maximum profit d p d x = 0 and d 2 p d x 2 < 0
d p d x = 0 2 x + 125 = 0 x = 62 5
Hence x = 62 5 give maximum profit.
P ( 62 5 ) = ( 62 5 ) 2 + 125 × 62 5 2200 = 1706.25 $
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