SOLUTION: PROFIT ANALYSIS A consultant hired by a small manufactur- ing company informs the company owner that their annual profit can be modeled by the function P(x) = -1.2x2 + 62.5

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Question 940049: PROFIT ANALYSIS A consultant hired by a small manufactur-
ing company informs the company owner that their annual profit
can be modeled by the function P(x) = -1.2x2 + 62.5x - 491
where x represents the number of employees and P is profit in thou-
sands of dollars. How many employees should the company have to
maximize annual profit? What is the maximum annual profit they
can expect in that case?
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
+p%28x%29=+-1.2x%5E2%2B62.5+x+-491

where x represents the number of employees and P is profit in thou-
sands of dollars.
dp%28x%29%2Fdx++=+%28d%2Fdx%29%2A+%28-1.2x%5E2%2B62.5x-491%29
=-2%2A1.2x%2B62.5
= -2.4x+62.5
make +dp%28x%29%2Fdx++=0 to find x where p(x) becomes maximum
-2.4x +62.5 =0
move -2.4 to the right
62.5 = 2.4 x
divide with 2.4 on both sides
+62.5%2F2.4++=2.4+x%2F2.4+
x= 26
No of employees = 26
Max profit , P(x) = +-1.2%2A+26%5E2+%2B62.5+%2A+26-491
p(x) = -811.2%2B1625-491
= 322.8 thousands dollars
= $ 322800