3. The Charm City Consultants Inc. wants to build a new network of computers for
ID: 2487772 • Letter: 3
Question
3. The Charm City Consultants Inc. wants to build a new network of computers for its employees. The management of the company is considering three network sizes for the possible purchase: large, medium, or small. The management believes that the demand for their services will be either high level, medium level, or low level. The payoff (profit in dollars) table for the situation is given below:
Demand Level
Decision High Medium Low
Large Size $150,000 $ 60,000 $20,000
Medium Size $100,000 $110,000 $50,000
Small Size $ 60,000 $ 70,000 $80,000
(a) What is the best decision using the maximax criterion? What is the payoff for it?
(b) What is the best decision using the maximin criterion? What is the payoff for it?
(c) What is the best decision using the minimax regret criterion? What is the payoff for it?
(d) What is the best decision using the Hurwicz’s criterion if = 0.4? What is the payoff for it?
Explanation / Answer
Answer 1.
Under Maximax criterion :
The maximum payoff is of $150,000 when demand is high under Large Scale.
Answer 2.
Under Maximin Criterion :
Minimum under Large size = 20,000
Minimum under medium size = 50,000
Minimum under small size = 60,000
So, the maximum under these minimum payoff is $60,000 under small size.
Answer 3.
Under Minimax Regret Criterion :
Maximum under Large size = 150,000
Maximum under medium size = 110,000
Maximum under small size = 80,000
So, the minimum under these maximum payoff is $80,000 under small size.
Answer 4.
Decision Large Size = 150,000 * 0.4 + 20,000 * 0.6 = 72,000
Decision Medium Size = 110,000 * 0.4 + 50,000 * 0.6 = 74,000
Decision Small Size = 80,000 * 0.4 + 60,000 * 0.6 = 68,000
So, Medium Size should be selected with payoff of $74,000.
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