The online retail operation you recently opened is doing well
but you are uncertain of your pricing strategy. Currently the typical customer
purchases four items at an average price of $11.96 and for an average
transaction size of $47.84. The cost of goods is 60 percent of sales, which
yields a gross margin of 40 percent. You are considering lowering prices by 10
percent across the board so you can better compete with other music e-tailers.
If you lower prices by 10 percent, you believe that the average number of items
purchased per customer would rise by 25 percent.

Review the scenario and address each question while showing work
for all mathematical problems. Provide full analysis for all conclusions
made.  For any assumptions made, be sure to reference the scenario when
providing justification for responses.