A manufacuturer sells instruments for 70 per unit. The cost of producing x instruments is C (x)=2000+4x+0.003x^2 and no more than 15000 instruments can be made in a week.Find themamount of instruments should be made to get max profit in a week.
profit = revenue-cost, so
p(x) = 70x - (2000+4x+0.003x^2) = -0.003x^2 + 66x - 2000
dp/dx = 66 - 0.006x
dp/dx=0 at x=11000