Exercise $1$:

A firm's average cost function is given as: $AC=-25+\frac{100}{Q}+3Q^2.$

a$)$ Calculate the total cost TC as a function of $Q.$

b$)$ Find the marginal cost when $Q=10.$

c$)$ Determine the value of $Q$ that maximizes the total cost.

d$)$ If the current output level is $Q=20,$ calculate the approximate change in the total cost if $Q$ increases by $2$ units.Exercise $1$:

A firm's average cost function is given as: $AC=-25+\frac{100}{Q}+3Q^2.$

a$)$ Calculate the total cost TC as a function of $Q.$

b$)$ Find the marginal cost when $Q=10.$

c$)$ Determine the value of $Q$ that maximizes the total cost.

d$)$ If the current output level is $Q=20,$ calculate the approximate change in the total cost if $Q$ increases by $2$ units.