Question 390216: A factory finds that it's daily profit, y dollars, is related to x, the number of items it produces daily where y = -x^2 + 90x.
a) Draw the graph of y = -x^2 + 90x.
b) Use this graph to find
i) the number of items the factory must produce daily in order to maximize profit,
ii) the maximum profit.
=)
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! A factory finds that it's daily profit, y dollars, is related to x, the number of items it produces daily where y = -x^2 + 90x.
a) Draw the graph of y = -x^2 + 90x.
b) Use this graph to find
i) the number of items the factory must produce daily in order to maximize profit,
At x = 45 it peaks and then drops.The maximum it should produce is 45 items.
From: mananth@hotmail.com
To: ahmad.tehseen@hotmail.com
Subject: RE: Thank you note (algebra.com problem 390216)
Date: Mon, 3 Jan 2011 21:29:58 +0530
Firstly you know that it is a parabola.
the co-efficient of x^2=- so the parabola opens downwards.
for y = 0 you have 2 values of x.
y =-x^2 +90x
y=-x(x-90)
x= 0 & x=90
you have two points (0,0) & (0,90)
.
find the vertex
x co-ordinate = -b/2a in the equation ax^2+bx +c
x co-ordinate= -90/-2
x co-ordinate = 45
..
when you put the equation in (x-h)^2 +k
you get the value of k which is the y co-ordinate of the vertex.
y= (-x^2+90x) -45^2 +45^2
y=-1(x^2-90x+45^2) +45^2
y=-1(x-45)^2+2025
vertex = (45,2025)
The y value when production = 45 units is 2025 . The maximum profit.
You have three values including vertex.
plot a few points with x <45 & > 45 . Find y co-ordinates . draw the curve.
Generally students use a graphic calculator to get the points.
(0,0) & (0,90) (45,2025)
ur mails are bouncing so I can't clarify your doubts
Happy new year
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