Q.The marginal cost of producing $x$ units is $MC=6x+5$ (in ₹ per unit), and the fixed cost is ₹200. Find the total cost function, and the cost of producing 10 units.

Integrating the marginal cost function and pinning the constant using the fixed cost recovers the total cost function.

Integrating the marginal cost

Pinning $K$ using the fixed cost

Since $C(0)=\text{Fixed Cost}=200$: $C(0)=3(0)^2+5(0)+K=K=200$.

Cost of producing 10 units

$C(10)=3(10)^2+5(10)+200=300+50+200=550$ …

Setting $K=0$ by mistake, as if this were a revenue function — total COST always has a non-zero constant equal to the fixed co …