A river located in Antalya is open to all fishermen so they can fishing freely. They shoud pay 10 dollar for a boat for fishing. The equation is f(n)= 90n^1/3. n is number of boats. Equation gives total number of sea bass caught and each boat catches f(b)/ b kg sea bass. The price of a sea bass is 1 dollar per kg.
Can you find the efficient number of boats
Can you find per boat tax would statisy efficiency .
Total cost for n boats = 10n
Total Revenue = 90(n)^1/3
Total profit = 90(n)^1/3 - 10n
for maximum : dP/dn =0
=> 90*(1/3)/n^2/3 -10 = 0
=> n^2/3 = 3
=> n = 3^1.5 = 3*1.7 = 5(approx)
efficient value = 90(5.1)^1/3 - 10(5) = 90*1.72 - 50 = 105
2) let tax = t
Total profit per boat = 90/n^2/3 -10
after tax this amount should be 90/n^2/3 - 10 - t
this amount should be 105/5 = 21
90/n^2/3 -t = 31
t = 90/(n^2/3) -21
A river located in Antalya is open to all fishermen so they can fishing freely. They...