Price of Widgets
Annual widget demand x (widgets)	Price per widget p ($/widget)
10	147
20	132
30	125
40	128
50	113
60	97
70	85
80	82
90	79
100	53

• Recall that revenue is related to price and the number of widgets sold. Assume that the annual widget sales match the annual widget demand, and construct a model for revenue using the model for price that you found in the Price section. Find the model for revenue R ( x ), where R ( x ) is the total annual revenue in dollars for x widgets sold, and write it as R ( x ) = a x 2 + b c + c. Note: You are using the fact that R ( x ) = x p ( x ), not creating a table of data.
• Use your revenue model to compute R ( x ) for certain values of x. Give the real-world interpretation of the result of each computation in complete sentences. Be sure to include units.
• Use your revenue model R ( x ) to determine the number of widgets that you should try to sell in order to maximize revenue. What is the maximum revenue? Be sure to answer in complete sentences and to include units. Explain how you found the results.

This what my result from Regression Project: Price

To estimate p(x) for x= 25, substitute 25 into -0.956*x +157

p(25) = -0.956*25+157

= -23.9 + 157

= 133.1 = 133

To estimate p(x) for x= 45, substitute 45 into -0.956*x +157

p(45) = -0.956*45+157

= -43.02 + 157

= 113.98 = 114

When price per widget increases from 113.98$ to 133.1$, the annual demand for widget decreases from 45 to 25 units.

for p(x) to be 0, that is,

-0.956*x +157=0

-0.956*x = -157

x = -157/(-0.956)

= 164.23 = 164

When the the annual demand for widget will reach at approximately 164.23 then price per widget will be 0$.