Question #224874

The Extraordinary Manufacturing Company has established that the relationship between sales price for one of its products and the quantity sold per month is approximately 3D=1680-39p units. The fixed cost is P1500 per month, the variable cost is P45 per unit produced.


  • What number of units should be produced and sold per month to maximize net profit? What is the maximum profit?
  • What is the production range of profitable business for the company?
1
Expert's answer
2021-08-12T05:09:37-0400

Given

3D=16803P3D=1680-3P

Fixed cost=1500

Variable cost=45

Rearrange

3D=16803D3P=16803DP=560D3D=1680-3D\\3P=1680-3D\\P=560-D

a)

Profit maximizing level

MR=MCTR=P×DTR=(560D)D2MR=dTRdD=5602DTC=1500+45DMC=dTCdD=45MR=MC\\TR=P×D\\TR=(560-D)D^2\\MR=\frac{dTR}{dD}=560-2D\\TC=1500+45D\\MC=\frac{dTC}{dD}=45

Now MR=MC

5602D=4556045=2DD=257.5P=560DP=560257.5=302.5560-2D=45\\560-45=2D\\D=257.5\\P=560-D\\P=560-257.5=302.5


Profit=TR-TC

TR=560DD2=560(257.5)(257.5×257.5)=14420066306.25=77893.75TR=560D-D^2\\=560(257.5)-(257.5×257.5)\\=144200-66306.25\\=77893.75

TC=1500+45D=1500+45(257.5)=1500+11.587.5=13087.5TC=1500+45D\\=1500+45(257.5)\\=1500+11.587.5\\=13087.5

Profit=77893.7513087.5=64806.25=77893.75-13087.5=64806.25


b)

Range=257.50.5=257257+0.5=258257258Range=257.5-0.5=257\\257+0.5=258\\257-258

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