  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 help_outlineImage Transcriptionclose1. 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
Step 1

(a) The given revenue and cost functions are, help_outlineImage TranscriptioncloseR(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. help_outlineImage TranscriptioncloseR(130) 120(130)-0.46(130) =15600 7774 - \$7826 Thus, the maximum revenue is \$7826 fullscreen
Step 3

(b)Find maximum... help_outlineImage TranscriptioncloseP(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

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