Tropical pools sells an aboveground model for p dollars each. The monthly
revenue from the sale of this model is given by
R=-0.08pē + 300p
revenue is the product of the price p and the demand (quantity sold).
A) Factor out the price on the right hand side of the formula
---------------------------
R = -.08pē + 300p
Do what it says and factor out p
R = p(-.08p + 300)
B) What is the expression of the monthly demand?
We reason this way:
We first notice that it says
"revenue R is the product of the price p and the demand (quantity sold)."
We know that "product of p and the demand" means that p is multiplied by
demand.
Therefore we know that revenue R means "p multiplied by demand".
Now we look at the formula for the revenue R
R = p(-.08p + 300)
and ask ourselves "What is p multiplied by in that formula?"
We look and see that right after p we see a parentheses with
(-.08p + 300).
So we say "Hey, in the formula for revenue R we see that
p is multiplied by (-.08p + 300)"
Then we look up there again where it says
"revenue R means "p multiplied by demand".
Then we reason "Well since the revenue R means "p multiplied by demand"
and we notice in the formula for revenue R has p next to and therefore
multiplied by (-.08p + 300), it must mean that the demand and (-.08p + 300)
are the same thing. So since they are the same thing, they must be equal,
so we write
DEMAND = -.08p + 300
C) What is the monthly demand for the pool when the price is $3000
Since p stands for price we plug in $3000 for p in the formula
DEMAND = -.08p + 300
DEMAND = -.08(3000) + 300
DEMAND = -240 + 300
DEMAND = 60
Since up there is says that the demand is the quantity sold, we
see that there must have been 60 sold.
Edwin
