Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
we have the quadratic equation
[tex]R(p)=-9p^2+18,000p[/tex]this is a vertical parabola, open downward
the vertex represents a maximum
Convert to factored form
Complete the square
factor -9
[tex]R(p)=-9(p^2-2,000p)[/tex][tex]R(p)=-9(p^2-2,000p+1,000^2-1,000^2^{})[/tex][tex]\begin{gathered} R(p)=-9(p^2-2,000p+1,000^2)+9,000,000 \\ R(p)=-9(p^{}-1,000)^2+9,000,000 \end{gathered}[/tex]the vertex is the point (1,000, 9,000,000)
therefore
Problem N 2
we have the equation
[tex]C(x)=0.7x^2+26x-292+\frac{2800}{x}[/tex]using a graphing tool
the minimum is the point (8.58,308.95)
therefore
Part a
the average cost is minimized when approximately 9 lawnmowers ........
Part b
the minimum average cost is approximately $309 per mower
