OPIM 4050 Supply Chain Management – Homework 7

Name(s):

1. North Adventures, a travel company, provides different nature expeditions and city travels. There are only 40 seats available for their Alaska Photo Tour Adventure. Currently, the company charges $2,500per person. At this price, all seats get booked about three months in advance. A group of customers have said that they would be willing to pay three times as much ($7,500 per seat) ifNorth Adventures had seats available one week before departure. About six months in advance, demand for customers who are willing to pay three times as much is normally distributed, with a mean of 16 and a standard deviation of 5.

a) You may use Excel or the table below. How many seats should North Adventures reserve for their Alaska Photo Tour Adventure for the high-price customers?

F-1(1 – pL/pH, , ) = F-1(1 – 2,500/7,500, 16, 5) = F-1(0.667, 16, 5) = 18.158

F-1(0.25,16,5) / 12.63
F-1(0.333,16,5) / 13.84
F-1(0.5,16,5) / 16.00
F-1(0.667,16,5) / 18.16
F-1(0.5,5,16) / 5.00
F-1(0.667,5,16) / 11.91

North Adventures has identified two customer segments for their main nature expedition the Canada Experience.One customer segment (1) prefers to make a reservation at the last minute and is price insensitive.Another customer segment (2) is willing to make a reservation weeks in advance, but is price sensitive. Assume that the cost incurred by North Adventures for organizing activities and making reservations is $1400 per person. Demand from segment 1 is represented by the demand curve d1 = 2,000 –p1 and demand from segment 2is represented by the demand curve d2 = 5,000 – 3p2.

b)Assume that there is no limit on the number of seats for the Canada Experience.If North Adventures charges the same price for both segments, what price would maximize their profits?

What is the optimal price to ask for both segments? What is the demand for both segments?

First, we need to aggregate the demand curves. The new demand curve is given by:

d = (2000 – p) + (5000 – 3p) = 7,000 – 4p

Hence, the optimal price for this demand curve is

p = A/(2B) + c/2 = 7000/(2*4) + 1400/2 = 875 + 700 = $1,575

c) What is the total profit for the Canada Experience if North Adventures charges the same price for each segment?

Profit = (p – c)(A – Bp)

= (1575 – 1400)(7000 – 4*1575)

= $122,500

d) Assume that there is no limit on the number of seats for the Canada Experience.If North Adventures chargesa different price for each segment, what price would maximize their profits?

For segment 1:

p1 = A1/(2B1) + c/2 = 2000/(2*1) + 1400/2 = 1000 + 700 = $1,700

For segment 2:

p2 = A2/(2B2) + c/2 = 5000/(2*3) + 1400/2 = 833.33 + 700 = $1,533.33

e) What is the total profit forthe Canada Experience if North Adventures charges a different price for each segment?

Profit = ∑for each segment i (pi – c)(Ai – Bipi)

= (1700 – 1400)(2000 – 1*1700) + (1533.33 – 1400)(5000 – 3*1533.33)

= 90000 + 53333.33

= $143,333.33