Question

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)

Answer 1

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=
`(400-280)/(5000-1000)`

=
`120/4000=0.03`

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

`280=0.03(1000)+b`

=>
`280=30+b`

=> b = 250

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

`p=0.03x+250`

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

`440=0.03x+250`

=>
`0.03x=440-250`

=>
`0.03x=190`

=> 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.

`p=0.03(0)+250`

=> p = $250