Question

Assume TC = 5Q2+ 200Q+ 110 is the cost function of a firm. This firm sells 30Q for a unit price of Rs. 10. What is the profit maximizing quantity of this firm?

Answer 1

Here, In the question cost function is given as

$TC= 5 Q^2 + 200 Q+110$

here from above function we can say that

TFC=110

ATC (Q)=$5Q+200+\frac{110}{Q}$

and TVC(Q)= $5Q^2+200Q$

AVC(Q)=200 +5Q

MC(Q) = 10Q+200

now we can say that if $P<200$ , production is zero

here,

firms selling= 300

so profit

P= 10 Q+200

$Q= \frac{P-200}{10}$ , this is profit maximization quantity of this firm