Function as mathematical model problem. pls. help?

Question

2,400 clocks would be sold if the whole sale price is 160 dollars

however if the price is reduced to 120 dollars, there would be 4800 clocks sold. assume that the relationship of the clock's price and expected units sold is linear.

a.) find the mathematical model expressing the wholesale price as a function of the number of clocks sold

b.) what would the price be if there is a demand of 3800 units?

please show complete solution, thank you very much!

Answer 1

You can do this graphically, or analytically.

Graphically:

Get some graph paper.

Label the horizontal axis "price", and scale it from 0 to 200

Label the vertical axis "number of clocks sold", scaled from 0 to 5000

Draw the point (160, 2400).

Draw the point (120, 4800).

Draw a straight line between them.

Now draw a horizontal line at 3800.  It will cross the diagonal line.  Where it crosses, draw a vertical line, all the way down to your price scale.  Read the number.

Analytically:

Your model is y = mx + b.

y is the number sold

x is the price.

Find the slope using:

m =  (number sold at price 2 - number sold at price 1) divided by (price 2 - price 1)=  (4800 - 2400) / (120 - 160) = -60.

Find the intercept using:

b = y - mx = (number sold at price 1) - m times  (price 1)= 12000.

(This is the number of clocks you'd be able to give away free when the price is 0).

Should be clocks sold = -60 times price + 12000.

For every dollar you raise the price, you'll sell 60 fewer clocks.

If you rearrange y = mx + b so that x is on the left side of the equals sign, and y, m and b are on the right side, you can find the price when y (demand) = 3800.

Answer 2

the relationship of the price and volume sold is not linear

Answer 3

Not really an engineering question

find the slope of the line created by

(4800 - 2400)/(120- 160) = -60

so as the price increases the number of units sold decreases.

so

(4800 - 3800)/(120-x) = -60

b. x =136.667 or approximately 137

a.  # of units sold = 60*(120-price of units)+4800