Question $5[20]$

A firm's total cost function is given by the equation: $TC=4000+12Q+10Q^2.$

$5\mathrm{.}1$ Write an expression for each of the following cost concepts:

$5\mathrm{.}1\mathrm{.}1$ Total fixed cost $4000$

$5\mathrm{.}1\mathrm{.}2$ Total variable cost $1201092$

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$5\mathrm{.}1\mathrm{.}3$ Average variable cost

$5\mathrm{.}1\mathrm{.}4$ Average total cost

$5\mathrm{.}1\mathrm{.}5$ Marginal cost

$5\mathrm{.}2$ Determine the quantity that minimises average total cost.

$5\mathrm{.}3$ Explain the relationship between marginal and average cost.