Re: desperate help needed


"renee" <reneesawrey@xxxxxxxxxxxxxxx> wrote in message
news:1192099515.075735.158230@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
hi.. I've never posted on this group before, but I am in year 12
in
maths b.. and have a maths homework question i just can't figure
out.
If anyone would be kind enough to explain how I can do this, I
would
greatly appreciate it.

The task is as follows:

"A man runs a unicycle hire service, and charges $12 per unicycle.
There is an average of 36 rentals each day. It is known that for
every
fifty cent increase in hire prices, the average unicycle business
can
expect to lose two rentals each day, and vice versa. Based on this
information, how can this man maximize his profits?"

I know that I need to differentiate the function and then set it
to
zero to find the maximum, yet I just can't find the function for
this
question.


Let
x=price per item (The original problem is not using word profit
correctly. I am replacing it with word sale)
y=quantity sold
sale = s =xy
Relation between x and y is linear with slope m. (why?)
m = -2/0.5=-4
Point (12, 36) lies on a st. line with slope m=-4.
Y intercept=84 (use y=mx+c)
eqn of st. line is y=-4*x+84
s=xy=-4x^2+84x
Reqd to find dy/dx=0=-8x+84=> x=10.5
Use test of second derivative. 2nd derivative is -8 <0 hence at
x=10.5 we have maxima.
Find corresponding quantity sold as y=42
Thus sales=s=10.5*42=441


--
Best regards

Mohan Pawar
MP Classes LLC
www.mpClasses.com
US Central Time: 9:15 AM 10/11/2007

.

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