Applications Of Derivatives Question 60
Question: The profit function, in rupees, of a firm selling x items $ (x\ge 0) $ per week is given by $ P(x)=-3500+(400-x)x $ . How many items should the firm sell so that the firm has maximum profit-
Options:
A) 400
B) 300
C) 200
D) 100
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ P(x)=-3500+(400-x)x= $ $ -3500+400x-x^{2} $
On differentiating w.r.t.x, we get $ P’(x)=400-2x $ Put $ P’(x)=0 $
for maxima or minima
$ \Rightarrow 400-2x=0 $
$ \Rightarrow x=200 $ Now $ P’’(x)=-2x $
$ \Rightarrow P’’(200)=-400<0 $
$ \therefore ,P(x) $ is maximum at $ x=200 $
Hence 200 items should the firm sell so that the firm has maximum profit.
BETA
