Question 880694: quadratic applications:
A Paper company has determined that when x Boxes of paper are produced,then the average cost of box of paper is given by
-> C(X)=0.1x^2-15.2x+579.1
where C(X)is the average cost in dollars. How many boxes should be produced in order to minimize the average cost? i am so confused we can use the graphing calc but i plug it in and nothing shows up also have to find the min or max value.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A Paper company has determined that when x Boxes of paper are produced,
then the average cost of box of paper is given by
C(X) = 0.1x^2 - 15.2x + 579.1
where C(X)is the average cost in dollars.
How many boxes should be produced in order to minimize the average cost?
:
C(x) = y, write the equation
y = 0.1x^2 - 15.2x + 579.1
we can find the minimum by finding the axis of symmetry, using
y = ax^2 + bx + c
The axis of symmetry: x = -b/(2*a), in this equation
a = .1; b=-15.2, so we hve
x = 
x = 
x = 76 boxes produces minimum unit cost
:
To find what the actual minimum cost is, replace x with 76 in the original equation.
C(x) = 0.1(76^2) - 15.2(76) + 579.1
Do the math
C(x) = $1.50 is the unit cost
:
:
To put his into you calc Ti83 or similar, y= enter 0.1x^2 - 15.2x + 579.1
Go to "window", select
xmin=-50
xmax=600
xsc1=10
ymin=-50
ymax=600
ysc1=50
Graph should look like this
The scale makes it hard to see y = 1.50 at minimum
:
Use the calc to find the min
Select Calc; select 3.minimum; leftbound, use the arrows to place cursor on the left min, hit enter
rightbound, use arrow to place cursor to the right of min, hit enter
Guess, hit enter again
It will displace x=76, y = 1.5, same as we got using axis of symmetry
:
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Did you understand all this? Let me know: ankor@att.net
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