Assignment

1. Assume that a firm accepts the following price-demand relationship as being a realistic representation of its market (Show mathematical steps in detail to receive full credits)

Ad = 400 - 5P

Where Ad= annual demand for a product in units P=price per unit
Where p must be between $20 and $70

a. How many units can the firm sell at the $20 per-unit price? At the $70 per-unit price?

b. What happens to annual units demanded for the product if the firm increases the per unit price from $26 to $27? From $42 to $43? From $68 to $69? What is the suggested relationship between per-unit price and annual demand for the product in units?

c. Calculate the mathematical equation for the total revenue (TR), which is the annual demand multiplied by the unit price. Make sure this equation should be a function of price (P)

d. Based on other considerations, the firm's management will only consider price alternatives of $30, $40, and $50. Use your equation from part (c) to determine the price alternative that will maximize the total revenue

e. What are the expected annual demand and the total revenue according to your recommended price?

2. It has been reported that 12,000 employees of Southwest Airlines are distributed among the following corporate functions. (20 points)

For the sample space consisting of Southwest employees, calculating the followings: (Show mathematical steps in detail to receive full credits)

a. What is the value of P(A)?
b. What is the value of ??(?? ∪ ??)?
c. What is the value of ??(?? ∪ ????)?
d. What is the value of ??(???? ∪ ??)?

3. Of employed U.S. teenagers age 17 or older, 90.4% have completed elementary school while 34% have completed middle school. For E=completed elementary school, M=completed middle school, and assuming that one must complete elementary school before completing middle school, calculate the following probabilities for an teenagers: (Show mathematical steps in detail to receive full credits)

a. ??(??)
b. ??(??|??)
c. ??(?? ∩ ??)
d. ??(?? ∩ ????)