A) The maximum revenue is 450000$
B) The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each
C) When each set is taxed at $55, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.
A)p(x)=300−(x/20),
revenue R(x)=p*x
revenue R(x)=300x -(x2/20)
for maximum revenue dR/dx =0 ,
=>300-(2x/20)=0
=>x/10=300
=>x=3000
maximum revenue = R(3000)=300*3000 -(30002/20)
maximum revenue = R(3000)=450000$
B) profit =revenue -cost
profit P(x)=300x -(x2/20)-72000-60x
profit P(x)=240x -(x2/20)-72000
for maximum cost dP/dx =0
240 -(2x/20)=0
x=240*10
x=2400
p(2400)=300−(2400/20)=180
profit P(2400)=240*2400 -(24002/20)-72000 =216000
The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each
c)
profit =revenue -cost -tax
profit P(x)=300x -(x2/20)-72000-60x-55x
profit P(x)=185x -(x2/20)-72000
for maximum cost dP/dx =0
185-(2x/20)=0
x=185*10
x=1850
p(1850)=300−(1850/20)=207.5
profit P(1850)=185*1850 -(18502/20)-72000
profit P(1850)=99125$
When each set is taxed at $55, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.
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