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Producers will make 1000 refrigerators available when the unit price is $280.00. At a unit price of $400, 5000 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 $440?______ refrigerators

What is the lowest price at which a refrigerator will be marketed? $_________ (lowest price)

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Answer:

For linear equations we use:

p=mx+b   ------  (1)

Now we have the following coordinates:

(x1,p1)= (1000,280) and (x2, p2)=(5000,400)

First we need slope (m)

m= [tex](400-280)/(5000-1000)[/tex]

= [tex]120/4000=0.03[/tex]

Now we will plug the value of m in the first equation

[tex]280=0.03(1000)+b[/tex]

=> [tex]280=30+b[/tex]

=> b = 250

Now plug into p=mx+b using only m=0.03 and b=250

[tex]p=0.03x+250[/tex]

When the unit price is $440, we can plug in 440 in for p;

[tex]440=0.03x+250[/tex]

=> [tex]0.03x=440-250[/tex]

=> [tex]0.03x=190[/tex]

=> x = 6333 refrigerators

The lowest price at which  a refrigerator will be marketed, we can find this by plugging x = 0 in p=mx+b.

[tex]p=0.03(0)+250[/tex]

=> p = $250

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