I need help with a math problem

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Sally found when she charged $75 the number of video tapings demanded per year was 80.  At a video taping price of $100, the demand dropped to 60.  Given that this is linear, find the demand equation.  Above what price will there be no demand? What is the maximum quantity demanded?

Nov 30th, 2015

Thank you for the opportunity to help you with your question!

To derive the demand equation, we must understand that price is on the y axis while quantity is on the x axis.

Therefore, the slope of the demand curve is given by (75-100)/(80-60) = -1.25

The equation is Y=-1.25x + c

where Y - quantity demanded, x-price and c is a constant

takong one point say (80,75) we have 75 = -1.25(80)+c ;c= 175

Therefore demand equation is Y = 175-1.25X

The price above which there will be no demand is the price when quantity demanded is zero or the Y-intercept.

Hence, Y=175-1.25(0) =175

When price goes beyond 175, demand is zero.

The maximum quantity demanded is the quantity demanded when price is zero or the X-intercept.

Hence 0=175-1.25X; 1.25X=175

X=175/1.25 = 140

Maximum demand is 140

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 30th, 2015

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