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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

 Feb 26, 2020
 #1
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+1

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

 

 

 

cool cool cool

 Feb 26, 2020

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