The prior probabilities for a loan are: p(s1) = 0.7 and p(s2…

The prior probabilities for a loan are: p(s1) = 0.7 and p(s2) = 0.3, where s1 is repay and s2 is default. The decision alternatives are: d1 – make loan, and d2 – do not make loan. The payoff table is as follows: s1 s2 d1 10000 -20000 d2 6000 6000 The firm can acquire sample information in the form of a credit report that has three possible outcomes: high (H), medium (M), and low (L). The relevant conditional probabilities are: p(H | s1) = 0.60, p(M | s1) = 0.30, p(L | s1) = 0.10 p(H | s2) = 0.10, p(M | s2) = 0.10, p(L | s2) = 0.80 Compute the expected value of the sample information. Would it be worthwhile to pay $1000 for the report? Show all work.

A company makes four juice products using apple, grape, and…

A company makes four juice products using apple, grape, and cranberry juice. Cranberry juice sells for $2.00 per quart, grape juice sells for $2.20 per quart, cranberry-apple juice (a blend of cranberry and apple juice) sells for $2.40 per quart, cranberry-grape juice (a blend of cranberry and grape juice) sells for $2.60 per quart. Each product is produced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of apple juice, 600 gallons of grape juice, and 800 gallons of cranberry juice. The cost per gallon is $1.60 for apple juice, $2.00 for grape juice, and $1.80 for cranberry juice. Cranberry juice must comprise at least 50% of the cranberry-apple juice product. Cranberry juice must comprise at least 40% of the cranberry-grape juice product. Cranberry juice may comprise no more than 60% of the cranberry-apple juice product. Cranberry juice may comprise no more than 60% of the cranberry-grape juice product. Cranberry-apple juice containers may comprise no more than 25% of the number of containers produced. The ratio of quart containers of cranberry-apple juice to cranberry-grape juice must be at least 7 to 5. Formulate a linear programming model that will determine the number of containers of each product to produce so as to maximize profit. .