SOLUTION: A company makes t-shirts and their research shows that that price and demand are related linearly:p=mx+b.They know that in order to sell 5 shirts they need to set the price at $37,

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Question 1145178: A company makes t-shirts and their research shows that that price and demand are related linearly:p=mx+b.They know that in order to sell 5 shirts they need to set the price at $37, and in order to sell 15 shirts they need to set the price at $17. Find the linear equation relating price to demand.

Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
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The demand function is the number of sold items as a function of price.


The slope of the demand function is the ratio of the increment of the number of the sold items to the increment of the price.


In this case, the increment of the number of the sold items is  5 - 15 = -10  and 

              the increment of the price is  37-17 = 20 dollars.


Therefore, the slope is   = -0.5 item per dollar.


Hence, the requested demand function is  d(p) = 5 - 0.5*(p-37).    (1)


CHECK.  At p = 37,  d(p) = d(37) = 5 - 0.5*(37-37) = 5 - 0.5*0 = 5 - 0 = 5 items.   ! Correct !

        At p = 17,  d(p) = d(17) = 5 - 0.5*(17-37) = 5 - 0.5*(-20) = 5 + 0.5*20 = 5 + 10 = 15 items.   ! Correct !  


Notice.   You may transform the found function  (1)  to any other equivalent form.


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