Q$-2$

Giant Screen TV$,$ Inc., is a Miami$-$based importer and distributor of $70-$inch screen HDTVs for residential and commercial customers. The price and cost functions of his business are given as below:P $=600-5$QTC $=80+25$Q $+0\mathrm{.}6$Q$^2$Use Cost Minimization Case for a Firm and answer the following questions:$($a$)$ Calculate level of output; total profit and marginal profit for the firm.$($b$)$ Prove that:$($i$)$ ATC $=$ MC $($ii$)$ Slope of ATC $=0$ Use Optimal Multi$-$plant Case for a Firm and answer the following questions:$($c$)$ Calculate level of output; total profit and marginal profit for the firm.$($d$)$ Calculate total number of plants for the firm.Use Profit Maximization Case for a Firm and answer the following questions:$($e$)$ Calculate level of output; total profit and marginal profit for the firm.$($f$)$ Prove that:$($i$)$ MR $=$ MC $($ii$)$ Slope of MR $<$ Slope of MC