Swan Valley Farms produces dried apricots, which it sells to two cereal producers – Kellogg’s and General Foods. Swan Valley forecasts that for the upcoming year Kellogg’s will want to purchase either 10 or 20 tons of dried apricots, and General Foods will want to purchase either 10, 20, or 30 tons.
Kellogg’s and General Foods order independently of each other. The following probability distributions are believed to hold: Kellogg’s Demand Probability General Food’s Demand Probability 10 tons 0.30 10 tons 0.30 20 tons 0.70 20 tons 0.40 30 tons 0.30 Swan Valley is currently contracting with local farmers for delivery of apricots for drying.
It takes approximately four pounds of apricots to produce one pound of dried apricots. Swan Valley can purchase apricots at $0.15 per pound; it costs an additional $0.02 to produce one pound of dried apricots.
Swan Valley’s contract with Kellogg’s and General Foods calls for purchase in units of 10 tons at a price of $1,500 per ton plus delivery cost. The drying process takes several weeks; therefore, Swan Valley must sign its contract with growers before it knows the exact amount that Kellogg’s and General Foods will be ordering.
If Swan Valley dries more apricots than its two customers demand, it will sell the surplus dried apricots to a food wholesaler at a price of $1,100 per ton, plus delivery. If Swan Valley produces fewer dried apricots than the two cereal manufactures demand, it can purchase additional dried apricots from a competitor at a price of $1,400 per ton.
Prepare a business report to Henry Swan, owner of Swan Valley Farms, giving your recommendation for the quantity of apricots he should contract for with the farmers.
Consider techniques for uncertainty – you are not certain if Henry is optimistic a pessimistic, so you best provide information for both criterion. Since he believes certain probabilities do exist, you will want to include alternatives for decision making risk. Also take notice of the demand numbers. Remember, each cereal company may purchase in any quantity shown in the table.
What is the minimum expected demand, what is the maximum expected demand, and what are the possible demands between minimum and maximum?
How do these demands affect the probabilities in the table?
Henry has been cultivating a relationship with people working for both of his customers and believes he may be able to pay for information. What is the expected value of this information and how much should Henry be willing to pay?
Prepare your report following the Quantitative Analysis approach.