(Solved):   could you please explain in simple steps how to solve it ? thanks  Xenophobic Car Pala ...

 

could you please explain in simple steps how to solve it ? thanks 

Xenophobic Car Palace (XCP) purchases late-model domestic automobiles at wholesale auctions and sells them in Charleston and Savannah. XCP's total cost is given by \( T C= \) \( 100\left(Q_{C}+Q_{S}\right)+\left(Q_{C}+Q_{S}\right)^{2} \). The demand in each city for such gems is given by \( Q_{C}= \) \( 1,000-2 P_{C} \) and \( Q_{S}=500-P_{S} \). If XCP price discriminates between the two cities, how many cars will it sell in Charleston and Savannah? a. \( Q_{C}=100, Q_{S}=50 \) b. \( Q_{C}=50, Q_{S}=100 \) c. \( Q_{C}=75, Q_{S}=75 \) d. \( Q_{C}=100, Q_{S}=100 \) e. \( Q_{C}=50, Q_{s}=50 \)