marginal cost is $C'(x) = 5 + \frac{10}{\sqrt{x}}$, it is known that producing 100 units costs 950$, how much would it be to produce 400 units?
from that I can calculate total cost function which is $C(x) = 5x + 20\sqrt{x}$
Is it enough to just plug in 400? Or should I plug in 100 and get 700\$ which means 250$ is fixed cost?
So should I plug in 400 and add 250 to the result?
Can anyone help me please?
Best Answer
When you integrate the marginal cost function, your total cost function should actually be $C(x)=5x+20\sqrt{x}+C$. You're given that at 100 units, the cost is $950:
$$C(100)=950=700+C \implies C=250$$ Now, plug in 400 units into $C(x)=5x+20\sqrt{x}+250$ to obtain the cost for producing 400 units.