Consider the marginal cost function $\backslash ($ C$^\{\backslash$prime$\}($x$)=200+10$ x$-0\mathrm{.}01$ x$^\{2\}\backslash ).$

a$.$ Find the additional cost incurred in dollars when production is increased from $150$ units to $200$ units.

b$.$ Find the additional cost incurred in dollars when production is increased from $500$ units to $550$ units.

a$.$ The additional cost incurred in dollars when production is increased from $150$ units to $200$ units is approximately

$($Do not round until the final answer. Then round to two decimal places as needed.$)$

b$.$ The additional cost incurred in dollars when production is increased from $500$ units to $550$ units is approximately

$($Do not round until the final answer. Then round to two decimal places as needed.$)$