i need help finding out this algrebra problem. i really need to find the revenue function. HELP?

Question

yOU ARE MANUFACTORING AND SELLING TWIDGETS AT A PRICE OF $16 EACH, and at that price we have been selling 200 twidgets per month. With each increase in price of $1 will cause 50 fewer twidgets to be sold. You have a variable cost of $900 per month, and a fixed cost of $8 per twidget.

Find the Revenue Function,
Total Cost Fucntion,
and
Profit Function.


CAN ANYONE HELP ME PLEASEEE?

Answer 1

You first need to find a function relating the number of twidgets sold to the selling price. We're told that each increase in price of $1 causes 50 fewer twidgets to be sold.

Let x denote the number of widgets sold, and let p denote the unit selling price. Then x=200 when p=16; x=150 when p=17; x=100 when p=18; etc. From graphing these points, or from previous experience with this kind of problem, you can tell that there is a linear relationship between p and x. So let p =mx + b. From knowing x=200 when p=16, and x=150 when p=17, we get the slope:

m = (17-16)/(150-200) = -1/50

So p = (-1/50) x + b. Since p=16 when x=200,

16 = (-1/50)(200) + b so b = 20 and

p = (-1/50) x + 20

That's the hardest part of this problem.

Revenue = (unit price) times (number sold at that price)

R(x) = p*x = (-1/50)x² + 20x

Total Cost = fixed cost + (quantity sold)*(production cost per twidget)
= 900 + 8x

(I think you have the terminology reversed. Fixed costs are costs like rent, insurance, etc., that occur no matter what the number of twidgets produced is. (Total) variable costs vary depending on the quantity produced (although the production cost per twidget may be constant, as it is here).)

Profit = Revenue - Total Cost

I leave the rest to you.