menu
bartleby
search
close search
Hit Return to see all results

1. The monthly revenue R earned by selling x lamps isR(x)= 120x-0.46xThe monthly cost of producing x lamps isC(x) 30.25r t 1000.a) How marny lamps must be sold to maximize revenue? What is the maximum revenue?(b) The profit P earned by selling x lamps is given byP(x) R(x)-C(x)How many lamnps must be sold to maximize profit? What is the maximum profit?

Question
1. The monthly revenue R earned by selling x lamps is
R(x)= 120x-0.46x
The monthly cost of producing x lamps is
C(x) 30.25r t 1000.
a) How marny lamps must be sold to maximize revenue? What is the maximum revenue?
(b) The profit P earned by selling x lamps is given by
P(x) R(x)-C(x)
How many lamnps must be sold to maximize profit? What is the maximum profit?
help_outline

Image Transcriptionclose

1. The monthly revenue R earned by selling x lamps is R(x)= 120x-0.46x The monthly cost of producing x lamps is C(x) 30.25r t 1000. a) How marny lamps must be sold to maximize revenue? What is the maximum revenue? (b) The profit P earned by selling x lamps is given by P(x) R(x)-C(x) How many lamnps must be sold to maximize profit? What is the maximum profit?

fullscreen
check_circleAnswer
Step 1

(a) The given revenue and cost functions are,

R(x)(120x-0.46x)
= 120-2(0.46x)
120-0.92.x
Apply 0 for R (x)
R(x)0
120 0.92x 0
x130 lamps
help_outline

Image Transcriptionclose

R(x)(120x-0.46x) = 120-2(0.46x) 120-0.92.x Apply 0 for R (x) R(x)0 120 0.92x 0 x130 lamps

fullscreen
Step 2

Approximately 130 lamps must to be sold for the maximum revenue.

Substitute 130 for x in revenue function to find the maximum revenue.

R(130) 120(130)-0.46(130)
=15600 7774
- $7826
Thus, the maximum revenue is $7826
help_outline

Image Transcriptionclose

R(130) 120(130)-0.46(130) =15600 7774 - $7826 Thus, the maximum revenue is $7826

fullscreen
Step 3

(b)Find maximum...

P(x) 120x-0.46x2 -30.25x -1000
=-0.46x89.75x-1000
P(x)(0.46x+89.75x -1000)
= -0.92x 89.75
Apply 0 for P (x)
P (x)0
-0.92x 89.75 =0
x83 lamps
help_outline

Image Transcriptionclose

P(x) 120x-0.46x2 -30.25x -1000 =-0.46x89.75x-1000 P(x)(0.46x+89.75x -1000) = -0.92x 89.75 Apply 0 for P (x) P (x)0 -0.92x 89.75 =0 x83 lamps

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Other

Sorry about that. What wasn’t helpful?