Consider a retailer considering a $33-$percent$-$off sale on blenders currently priced at $$54.$ The retailer pays $$29$ per blender from the manufacturer.

a$.$ What is the initial contribution margin?

b$.$ What is the proposed sale price and the percent change in price captured per unit sold?

c$.$ What is the volume hurdle that must be achieved for the sale on blenders to improve profits through the sale of blenders alone?

d$.$ Suppose that instead of having this sale, a young pricing expert suggested that the price of Elenders be increased to $$59.$ What would be the allowable loss in sales of blenders that would still leave the retailer in a more profitable position?