MANASCI ASSIGN#1:  DECISION THEORY 

1.  Decision-Making Under Uncertainty

QUESTION:
Gabriel Goleb is considering the purchase of two types of industrial robots. The Rob1 (alternative 1) is a large robot capable of performing a variety of tasks, including welding and painting. The Rob2 (alternative 2) is a smaller and slower robot, but it has all the capabilities of Rob1. The robots will be used to perform a variety of repair operations on large industrial equipment. Of course, Gabriel can always do nothing and not buy any robots (alternative 3). The market for the repair could be either favorable (event 1) or unfavorable (event 2).  Under a favorable market, the expected returns for Alternatives 1, 2, and 3 are Php50,000, Php30,000, and none, respectively.   On the other hand, under an unfavorable market, the expected returns for Alternatives 1, 2, and 3 are -40,000, -20,000, and 0, respectively. Gabrriel is not confident about the probability of a favorable or unfavorable market.  The Hurwicz coefficient should be 0.7.  

Requirements:
a.)	Construct the payoff table
b.)	Determine the maximax, maximin, Laplace, and Hurwicz decisions. (Note: Please encircle the decision and put an extra column in your table to write your decision).
c.)	Construct the regret table
d.)	Determine the minimax regret decision.  (Note: Please encircle the decision and put an extra column in your table to write your decision).

2.  Decision-Making under Risk

Question:
Konik Foto is a small supplier of chemicals and equipment that is used by some photographic stores to process 35-mm film.  One product that Konik Foto supplies is AC-5.  Henry Garcia, president of Konik Foto, normally stocks 12, 13, 14 cases each week.  For each case that Henry sells he receives a profit of P350.  Because AC-5, like any photographic chemicals, has a very short shelf life, if a case is not sold by the end of the week, Henry must discard it.  Since each case costs Henry P560, he loses P560 for every case that is not sold by the end of the week.  There is a probability of 0.45 of selling 12 cases, a probability of 0.35 of selling 13 cases, and a probability of 0.20 of selling 14 cases.

Requirements:
a.)	Construct the payoff table
b.)	What is your recommended course of action to maximize expected profit and how much would the maximum EV be (show solution using both the expected value analysis and marginal analysis)?
c.)	Is it worth paying P4,500 for an accurate forecast of the weekly demand levels? Justify your answer.
d.)	If Henry Garcia is able to develop the remaining AC-5 with an ingredient that stabilizes it so it can be disposed at a bargain price of P500 per case by the end of the week, how would this change your recommended course of action?  What would be the max EV? It will cost him an additional P40 for the ingredient per case.
Clue:  Marginal Loss = Variable Cost – Salvage Value (if any)