SOLUTION: A small canteen offers special meal package to their customers. The profit P that the canteen will earn at x number of customer is modeled by the function P(x) = -25x2 + 100x - 3

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A small canteen offers special meal package to their customers. The profit P that the canteen will earn at x number of customer is modeled by the function P(x) = -25x2 + 100x - 3      Log On


   

Question 1170670: A small canteen offers special meal package to their customers. The profit P that the canteen will earn at x number of customer is modeled by the function P(x) = -25x2 + 100x - 3000. How many people are needed for a profit of atleast
Php5,000
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

P%28x%29+=+-25x%5E2%2B+100x+-3000
Differentiating w.r.t x :
P'%28x%29+=+-50x+%2B+100
+-50x+%2B+100+=+0
50x+=+100
x+=+2
P''%28x%29+=+-50+%3C+0
=> P%28x%29 is maximum at+x+=+2
Maximum profit = -25%2A2%5E2+%2B+100%2A2+-+3000
=+-2900
Canteen suffers a minimum loss of Php 2900.
There is no+way+to earn profit of Php+5000.


Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
A small canteen offers special meal package to their customers. The profit P that the canteen
will earn at x number of customer is modeled by the function P(x) = -25x2 + 100x - 3000.
How many people are needed for a profit of atleast
Php5,000
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In this problem,  the profit

            P(x) = -25x^2 + 100x - 3000 = (-25x^2 + 100x - 100) - 3000 + 100 = -(5x-10)^2 - 2900

is  NEVER  a positive value - it  ALWAYS  is negative.


The problem itself  HAS  NO  ANY  SENSE.

It is a  FAKE  created by mathematically illiterate person.

See the plot below.





                Plot y = -25x^2 + 100x - 3000