Thread: Refrigerator consumption

The monthly demand model for a refrigerator is given by N = -8p + 20000. The monthly supply model for the same refrigerator is N = 10p + 4250. For these models, p is the price of the refrigerator and N is the number of refrigerators sold or supplied each month by the store. Find the price at which supply and demand are equal (break-even point). At this price, how many refrigerators can be supplied and sold each month?

Monthly demand: Nd = -8p + 20000.

Monthly supply: Ns = 10p + 4250

When the two are equal,
Nd = Ns
-8p +20,000 = 10p +4,250
20,000 -4,250 = 10p +8p
15,750 = 18p
p = 15,750 / 18
p = 875 -------***

That means at break-even point, the price per refrigerator is 875. (in dollars or whatever. Not mentioned in the problem.)

----------------------------------
Substitute that in, say, Nd,
Nd = -8(875) +20,000 = 13,000

In Ns,
Ns = 10(875) +4,250 = 13,000 ----same, OK.

Therefore, at brake-even point, 13,000 refrigerators have to be supplied and sold at 875 each.