Cost-to-loss ratio problem. Consider the decision problem shown in Figure 5.26.
ID: 3276249 • Letter: C
Question
Cost-to-loss ratio problem. Consider the decision problem shown in Figure 5.26. Please read the attached image for the rest of the question. The first chunk of test just gives a backstory, the real question to be answered is in the second chunk of text. Please explain the question in detail so that I can understand it.
-5.6. Cost-to-loss ratio problem. Consider the decision problem shown in Fiue 5.26. This basic decision tree often is called a cost-to-loss ratio problem and is characterized as a decision situation in which the ques- tion is whether to take some protective action in the face of possible adverse circumstances. For example, the umbrella problem (Figure is a cost-to-loss ratio problem. Taking the umbrella incurs a fixed cost and protects against possible adverse weather. A farmer may face a cost- to-loss ratio problem if there is a threat of freezing weather that could damage a fruit crop. Steps can be taken to protect the orchard, but they are costly. If no steps are taken, the air temperature may or may not become cold enough to damage the crop 4.9)Explanation / Answer
It is an simple algebra problem where we know that how much loss we can bear if we take no action. Here in given examples, like buying umrella or not, it will depend on the probability that how much rainfall occurs in that certain place. Similarly, for a farmer to take precautionary measure to protect is orchard from freezing weather, it depend on the probability of freezing weather.
so, Let say protective action required a fixed amount of C.
and if we dont take preventive action, and any mishappening occured we incurred a loss and that loss is L
so Expected loss = L * p + 0 * (1-p) = pL ( where p is the probability of that misshappening)
so to take protective action
pL > C
so p > C/L
so p can at most be large as large as C/L before we have to take protective action.