A Partnership Between Dude Ranches and Mobile Homes

Dude Ranches Incorporated was founded on the idea that many families in the eastern and southern areas of the United States do not have a sufficient amount of vacation time to drive to the dude ranches in the Southwest and Rocky Mountain areas for their vacations. Various surveys indicated, however, that there was a considerable interest in this type of family vacation, which includes horseback riding, cattle drives, swimming, fishing, and the like. Dude Ranches Incorporated bought a large farm near several eastern cities and constructed a lake, a swimming pool, and other facilities.

However, to build a number of family cottages on the ranch would have required a considerable investment. Furthermore, they reasoned that most of this investment would be lost should the ranch-farm complex be a financial failure. Instead, they decided to enter into an agreement with the Mobile Homes Manufacturing Company to supply a very attractive authentic ranch-type mobile home. Mobile Homes agreed to deliver a mobile home on Saturday for $300 a week.

Mobile Homes must know early Saturday morning how many mobile homes Dude Ranches Incorporated wants for the forthcoming week. They have other customers to supply and can only deliver the homes on Saturday. This presents a problem. Dude Ranches will have some reservations by Saturday, but indications are that many families do not make them. Instead, they prefer to examine the facilities before making a decision. An analysis of the various costs involved indicated that $350 a week should be charged for a ranch home, including all privileges. The basic problem is how many mobile ranch homes to order from Mobile Homes each week.

Should Dude Ranches Incorporated order 10 (considered the minimum), 11, 12, 13, or 14 (considered the maximum)?

Any decision made solely on the information in the payoff table would ignore. However, the valuable experience that Dude Ranches Incorporated has acquired in the past four years (about 200 weeks) actually operating a dude ranch in the Southwest. Their records showed that they always had nine advance reservations. Also, they never had a demand for 15 or more cottages. The occupancy of 10, 11, 12, 13, or 14 ranch cottages, in part, represented families who drove in and inspected the facilities before renting. A frequency distribution showing the number of weeks in which 10, 11 -14 ranch cottages were rented during the 200-week period is found in the following table.
Number of Cottages Number of Rented Weeks
10 26
11 50
12 60
13 44
14 20
200

a. Construct a payoff table.
b. Determine the expected payoffs, and arrive at a decision.
c. Set up an opportunity loss table.
d. Compute the expected opportunity losses, and arrive at a decision.
e. Determine the value of perfect information.