+318 A manufacturer of slacks has discovered that the number x of khakis sold to retailers per week at a price p dollars per pair is given by the formula, p= 27- (x/400)^2
(a) Write the weekly revenue R(x) as a function of x.
(b) What is the domain of the nonnegative function R(x)?
(c) Graph y equals=R(x) on its domain
+128448 p = 27 - (x/400)^2 = [ 27 - x^2 / 160000]
(a) The revenue function for a week is price * pairs sold = p * x = 27x - x^3/160000
(b) The domain is [0, c]
And we can find c as follows
27x - x^3/160000 = 0
x ( 27 - x^2 / 160000) = 0
x = 0 is one solution [ we know this ]
And
27 = x^2 / 160000 = 0
27 = x^2 /160000
(160000)(27) = x^2 take the positive root
x ≈ 2078 = c
So the domain is [ 0, 2078 ]
(c) Here is the graph :
https://www.desmos.com/calculator/suhpihdav5
