$($a$)$ Find the average$-$cost function. The average$-$cost function is $\backslash (\backslash$overline$\{\backslash$mathrm$\{$C$\}\}(\backslash$mathrm$\{$x$\})=\backslash ).($b$)$ Find and interpret the average cost at sales levels of $2000$ hotdogs and $6000$ hotdogs. The average cost at sales levels of $2000$ hotdogs is $\backslash (\backslash$$ $\backslash )/100$ hotdogs. $($Round to the nearest cent as needed.$)$ The average cost at sales levels of $6000$ hotdogs is $\backslash (\backslash$$ $\backslash )/100$ hotdogs. $($Round to the nearest cent as needed.$)$ Interpret these results, choose the correct answer below. Take the sales level of $2000$ hotdogs as an example. Select the correct choice below and fill in the answer box to complete your choice.A$.$ At a sales level of $2000$ hotdogs, the average cost is $\backslash (\backslash$$ $\backslash )$ per $100$ hotdogs.B$.$ At a sales level of $2000$ hotdogs, if an additional $100$ hotdogs are sold, the average cost increases by approximately $\backslash (\backslash$$ $\backslash )$ per $100$ hotdogs. $($c$)$ Find the marginal average$-$cost function. The marginal average$-$cost function is $\backslash (\backslash$overline$\{\backslash$mathrm$\{$C$\}\}^\{\backslash$prime$\}($x$)=\backslash ).($d$)$ Find and interpret the marginal average cost at sales levels of $2000$ hotdogs and $6000$ hotdogs. The marginal average cost at sales levels of $2000$ hotdogs is $\backslash (\backslash$$ $\backslash )/(100$ hotdogs$)\backslash (\{\}^\{2\}\backslash ).($Round to the nearest cent as needed.$)$ The marginal average cost at sales levels of $6000$ hotdogs is $\backslash (\backslash$$ $\backslash )((100$ hotdogs$)\backslash (\{\}^\{2\}\backslash ).($Round to the nearest cent as needed.$)$ Interpret these results, choose the correct answer below. Take the sales level of $2000$ hotdogs as an example. Select the correct choice below and fill in the answer box to complete your choice.A$.$ At a sales level of $2000$ hotdogs, if an additional $100$ hotdogs are sold, the average cost decreases by approximately $\backslash (\backslash$$ $\backslash )$ per $100$ hotdogs.B$.$ At a sales level of $2000$ hotdogs, the average cost is $\backslash (\backslash$$ $\backslash )$ per $100$ hotdogs.