Problema Solution
Producers will make 1000 refrigerators available when the unit price is $330.00. At a unit price of $410, 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 $470?
refrigerators
What is the lowest price at which a refrigerator will be marketed?
$ (lowest price)
Answer provided by our tutors
For linear quations we use
P=mx+b.
We can treat our information as cordinates
(x1,p1)= (1000,330) and (x2, p2)=(5000,410).
First we need slope (m). To find slope we use the slope= (p2 − p1) / (x2 − x1)
m= (410-330)/(5000-1000)=80/4000=0.02
Using either cordinates plug p,x, and m, into p=mx+b and solve for B.
330=0.02(1000)+b simplify
330=20+b, b=310
Now plug into p=mx+b using only m=0.02 and b=310
p=0.02x+310
When the unit price is $470
Using the answer to the first question P=0.02x+310 we can plug in 470 in for P (price)
470=0.02x+310 simplify
160=0.02x
x=8,000 refrigerators
The lowest price
Using the same formula p=mx+b the price is lowest when quantity is at 0.
plug 0 in for x.
p=0.02(0)+310
p=$310 (lowest price)