1 Keeney and Raiffa (1976) discuss the assessment of a blood bank's multiattribute utility function. For...

 

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1 Keeney and Raiffa (1976) discuss the assessment of a blood bank's multiattribute utility function. For simplicity, we assume that the blood bank must determine at the beginning of each week how many pints of blood should be ordered. Any blood left over at the end of the week spoils (it is outdated). For the blood bank, two attributes of interest are as follows: Attribute 1 Number of pints of blood by which ordered blood falls short of the week's demand (the weekly short- age). The weekly shortage is known to be always between 0 and 10 pints. Attribute 2 Number of pints of blood that are outdated (known to be always between 0 and 10 pints) Assume that attributes 1 and 2 exhibit mui. a Suppose the blood bank is indifferent between 40 0, 0 1 0, 10 and .60 and between .50 0, 0 1 10, 0 and .50 Let x1 = value of attribute 1, and x2 = value of at- tribute 2. Also suppose that u(x1) .58 exp 1 .58 10 and uz(x2) = 1 – 100 %3| Determine the blood bank's multiattribute utility function. b Suppose that each week there is a chance that the demand for blood will be 25 pints and a chance it will be 35 pints. Would the blood bank be better off order- ing 28 pints, 30 pints, or 32 pints? 1 Keeney and Raiffa (1976) discuss the assessment of a blood bank's multiattribute utility function. For simplicity, we assume that the blood bank must determine at the beginning of each week how many pints of blood should be ordered. Any blood left over at the end of the week spoils (it is outdated). For the blood bank, two attributes of interest are as follows: Attribute 1 Number of pints of blood by which ordered blood falls short of the week's demand (the weekly short- age). The weekly shortage is known to be always between 0 and 10 pints. Attribute 2 Number of pints of blood that are outdated (known to be always between 0 and 10 pints) Assume that attributes 1 and 2 exhibit mui. a Suppose the blood bank is indifferent between 40 0, 0 1 0, 10 and .60 and between .50 0, 0 1 10, 0 and .50 Let x1 = value of attribute 1, and x2 = value of at- tribute 2. Also suppose that u(x1) .58 exp 1 .58 10 and uz(x2) = 1 – 100 %3| Determine the blood bank's multiattribute utility function. b Suppose that each week there is a chance that the demand for blood will be 25 pints and a chance it will be 35 pints. Would the blood bank be better off order- ing 28 pints, 30 pints, or 32 pints?

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