Amandas flower shop gets very busy on valentines day but the

Amandas flower shop gets very busy on valentines day, but they don\'t always sell out. Amanda knows that she can sell 50 rose bouquets at a price of 75$ each, but she can sell 60 if she drops the price to 65$ each. a) find the demand function p(x) assume its linear b) find the revenue function R(x) c Find for which the value(s) of x the marginal revenue equals to 0 d Suppose each boquet costs Amanda 25 $ to make. Find the marginal profit for x= 50 What does this value mean? Thanks for the help

Solution

a) demand function = we have points (50,75) and (60,65) (y-75)/(x-50) = (65-75)/(60-50) = -1 y-75 +x-50 = 0 y = -x + 125 b) revenue = y(x)*x = -x^2 + 125x c) so this will be =0 when y(x)= 25 so x= -y+125 = 100 d) marginal profit for x=50 value of y = 75 margin = 75-25 =50 so marginal revanue = 50*50 =2500 this means if she sells 50 roses then she\'ll have profit of 2500$