Construct Dr. Scriber’s decision tree diagram, using the proposed payoff measure.

Biotechnical Engineering specializes in developing new chemicals for agricultural applications. The company is a pioneer in using the sterile-male procedure to control insect infestations. It operates several laboratories around the world that raise insects and expose them to extra-large doses of radiation, making them sterile. As an alternative to chlorinated hydrocarbon pesticides, such as DDT, the sterile-male procedure has been used frequently with a good track record of success, most notably with the Mediterranean fruit fly (or Medfly). That pest was controlled in California through the release of treated flies on the premise that the sterile male flies would compete with fertile wild males for mating opportunities. Any female that

has mated with a sterile fly will lay eggs that do not hatch. The California Medfly campaigns required about five successive releases of sterile males—at intervals timed to coincide with the time for newly hatched flies to reach adulthood—before the Medfly was virtually eliminated. (Only sterile flies were subsequently caught in survey traps.) The effectiveness of the sterile-male procedure was enhanced by the release of malathion poisonous bait just a few days before each release, cutting down on the number of viable wild adults. More recently, Biotechnical Engineering has had particular success in using genetic engineering to duplicate various insect hormones and pheromones (scent attractants). Of particular interest is the application of such methods against the Gypsy Moth, a notorious pest that attacks trees, company has developed synthetic versions of both hormones and pheromones for that moth. It has a synthetic sexual attractant that male moths can detect at great distances. Most promising is the synthetic juvenile hormone. The juvenile hormone controls moth metamorphosis, determining the timing for the trans-formation of a caterpillar into a chrysalis and then into an adult. Too much juvenile hormone wreaks havoc with this process, causing caterpillars to turn into freak adults that cannot reproduce. Biotechnical Engineering has received a government contract to test its new technology in an actual eradication campaign. The company will participate in a small-scale campaign against the Gypsy Moth in the state of Oregon. Because the pest is so damaging, Dr. June Scribner, the administrator in charge, is considering using DDT as an alternative procedure. Of course, that banned substance is only available for government emergency use because of the environmental damage it may cause% in addition to spraying with DDT, two other procedures may be employed: (I) using Biotechnicals scent lure, followed by the release of sterile males, and (2) spraying with the company’s juvenile hormone to prevent larvae from developing into adults. Dr. Scribner wants to select the method that yields the best expected payoff, described below. Although both of the newer procedures are known to work under laboratory conditions, there is some uncertainty about successful propagation of the chemicals in the wild and about the efficacy of the sterile-male procedure with moths. If the scent-lure program is launched at a cost of $5 million, Biotechnical claims that it will have a fifty-fifty chance of leaving a low number of native mates versus a high number. Once the results of that phase are known, a later choice must be made to spray with DDT or to release sterile males; the cost of the .sterilization and delivery of the insects to the countryside is an additional $5 million. But if this two-phase program is successful, the net present value of the worth of trees saved is $30 million, including the benefit of avoiding all other forms of environmental damage. The indigenous moth population would be destroyed, and a new infestation could occur only from migrants. Biotechnical’s experience with other eradication programs indicates that if the scent lure leaves a small native male population, there is a 90% chance for a successful eradication by using stent, males: otherwise, there is only a 10% chance for success by using sterile males. A failure results in no savings. The cost of synthesizing enough juvenile hormone is $3 million. Biotechnical maintains that the probability that the hormone can be effectively disseminated is only 0.20. If it works, the worth of the trees saved and environmental damage avoided will be $50 million. This greater level of savings possible because of the permanent nature of the solution because a successful juvenile hormone ca-then be applied wherever the moths are known to exist, virtually eliminating the pest from the environment. But if the hormone does not work, the DDT must still be used to save the trees. DDT constitutes only a temporary solution. and the worth of its savings in trees is far less than the worth of either of the esoteric eradication procedures—if they prove successful. To compare alternatives, Dr. Scribner proposes using the net

advantage (crop and environmental savings. cost) relative to where she would be were to decide to use DDT at the outset or were

to be forced to spray with it later. (Regardless of the outcome, Biotechnical wilt be reimbursed for all expenditures. The decision is hers. not the Company’s.)

2. Construct Dr. Scriber’s decision tree diagram, using the proposed payoff measure.

3. What action will maximize Dr. Scribner’s expected payoff?

4. Dr. Scriber is concerned about assumed fifty-fifty probability for the two levels of surviving native males following the scent-lure program.

a. Redo the decision tree analysis to find what action will maximize Dr. Scriber’s expected payoff when the probability of low native males is, successively, (1) .40 or (2) .60 instead.

b. How is the optimal action affected by the probability level assumed for the low native male outcome?

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