Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.

Question

Producers of a certain brand of refrigerator will make 1600 refrigerators available when the unit price is $220. At a unit price of $270, 5600 refrigerators will be marketed. Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.
p = ?

 

How many refrigerators will be marketed when the unit price is $320?

 

What is the lowest price at which a refrigerator will be marketed?

Answer 1

Hi! You are looking for the equation of a line that represents number of units marketed (call this number N) as a function of price, which we can call p. Since you know this relationship between N and p is linear, we find the slope of the line and use it with either point in a Point-Slope equation for the line. We'll then use the equation to answer both the details you mention. Slope is (5600 - 1600)/(270 - 220) = 80 refrigerators per dollar of price. The Point-Slope equation of the line is: (N - 1600) = 80(p - 220) or N = 80p - 16000 So, when p = 320, N = 80(320) - 16000 = 9600 units will be made available, and the lowest price for which N = 1 refrigerator will be marketed is: 1 = 80p - 16000, and p = $200.01 Sincerely Yours, Joe F.