Question $5.$ A firm$$s total cost function is given by the equation:

TC $=4000+5$q $+10$q$2$

$($i$)$Write an expression for each of the cost concept:

$($a$)$ Total fixed cost;

$($b$)$ Average fixed cost;

$($c$)$ Total Variable cost;

$($d$)$ Average variable cost;

$($e$)$ Marginal cost.

$($ii$)$ Determine the quantity of output that minimizes average total cost. What is the minimum ATC? What is MC at minimum ATC?