A fur dealer find that when coats sell for $3200, monthly sales are 70 coats, when the price increases to $3500 the demand is for 20 coats. Assume that the demand equation is linear.
a) Find the demand and revenue equations ( interms of x, the number of coats sold monthly)
the demand equation is p=
and the revenue equation is R(x)=
Knowing that the demand quation is linear means that it will follow the form:
y=mx+b, where in this case y=p
We can use the given data to solve for m, the slope:
Therefore, for every 6 dollar increase in price, one less coat is sold.
Substituting in one of the known points, we cna solve for b, the y-intercept:
`3500=-6(20)+b -gt b=3500+120=3620`
Therefore, at a cost of $3620, no coats will be sold.
Therefore the demand equation is:
The equation for revenue will be equal to the price per coat multiplied by the number of coats sold: