An athletic shoe company is developing a new running shoe. The preliminary marketing analysis

indicates price$/$demand relationship as P$=$$$250-6$D$.$

The fixed cost is minimal as the company uses excess manufacturing capacity and could be as

low as $$10000.$ The variable cost per unit is estimated to be $$30.$

a$)-$ What is the range of production volume if the company intends to be profitable?

b$)-$ What is the optimum production volume to maximize profit?

c$)-$ If the company drops the price by $10\%,$ demand increases by $2\%.$ What conclusion do you

get from this exercise about the nature of the market this company is engaging in$?$