# Determine a total cost of producing x units

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? ## 1 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.