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.
If overhead is $2000 per month and the production cost per coat is $500, find the cost equation and the profit equation.
the cost equation is C(x)=
and the profti equation P(x)=
(be sure the equation are simplified)
find the level of production that maximizes profit
the level of production is=
The cost equation will be equal to the overhead plus the production cost, which is equation to 500 multiplied by the number of coats sold (x):
C(x)=2000 + 500x
The profit equation will be equal to the price of the coats multiplied by the number of costs sold minus the cost equation:
Next we must find the demand equation, p. We know that it is a linear function therefore:
First we solve for the slope, m:
Next we solve fot the y-intercept, b:
`3500=-6(20)+b -gt b=3500+120=3620`
Therefore the price per coat (p) as a function of the number coats sold is (x):
Substituting this into the profit equation above we find that:
In order to determine the level of production that maximizes profit we must find the value of x for which the derivative of the profit function is 0:
Therefore, if 260 coats are produced than profit is maximized.