In a skateboard factory, marginal cost decreases as more are made. Marginal cost for making x skateboards a month, dollars per board, is C'(x)=20/(√(1+0.04x)). Given that fixed costs are 2000, how much would it cost to make 200 boards in a month? I thought the answer was 5000 but I am wrong and now a bit confused as to why and what it actually would be.

Question

In a skateboard factory, marginal cost decreases as more are made.  Marginal cost for making x skateboards a month, dollars per board, is C'(x)=20/(√(1+0.04x)).  Given that fixed costs are 2000, how much would it cost to make 200 boards in a month?  I thought the answer was 5000 but I am wrong and now a bit confused as to why and what it actually would be.

oobleck · Accepted Answer

∫20/(√(1+0.04x)) dx = 1000√(x/25 + 1) + C since C(0) = 2000, 1000 + C = 2000 and C = 1000 C(x) = 1000√(x/25 + 1) + 1000 C(200) = 1000*3 + 1000 = 4000 Maybe you thought that C=2000 because that's the fixed cost?