Question $18(2$ points$)$

Simpson Flanders, Inc. $is$ a Motor City manufacturer and distributor $of$ valves used $in$ nuclear power plants. $In$ the past, all output was sold $to$ customers $in$ North American. Demand and marginal revenue curves for the firm are $as$ follows:

$P=1000-0\mathrm{.}015Q$

$MR=1000-0\mathrm{.}03Q$

Relevant total cost, marginal cost, and profit functions are:

$TC=1,500,000+600Q+0\mathrm{.}005Q^2$

$MC=600+0\mathrm{.}01Q$

Profit $=-1,500,000+400Q-0\mathrm{.}02Q^2$

Suppose that the firm was reorganized into two independent profit centers $(M=$manufacturing and $D=$ distribution$)$ with the following cost conditions:

$T{C}_M=1,250,000+500Q+0\mathrm{.}005Q^2$

$M{C}_M=500+0\mathrm{.}01Q$

$T{C}_D=250,000+100Q$

$M{C}_D=100$

Now assume that a major distributor $in$ the European market offers $to$ buy $as$ many valves $as$ Simpson Flanders wishes $to$ offer $at$ a price $of$ $$645.No$ impact from the company's North American customers $is$ expected and current facilities can $be$ used $to$ supply both markets.

Report the profit$-$maximizing price for the North American market. Report your solution out $to$ exactly two decimal places.