Question

CASE 2 A manufacturer is considering three decision alternatives: do nothing, sell the firm, and modernize the line. Doing nothing can generate a profit of $31 under strong economy but a loss of $12 under weak economy. Selling the firm regardless of the economy will generate $11. Modernizing the line can produce an attractive $56 profit if the economy is strong but a massive loss of $45 if the economy is weak. [3 points] What is the optimal decision using the minimax approach? Show your work [3 points] What is the optimal decision and expected value for 30% chance of strong economy?

Answer 1

Solution as per the Minimax ( or Minimax regret criteria).

Step 1: Prepare a payoff table.

Alternatives	Strong economy	Weak Economy
Do nothing	31	-12
Sell the firm	11	11
Modernize the line	56	-45

Step 2: Prepare a regret table and identify the maximum regret for each alternative.

Regret Table			Maximum Regret
Alternatives	Strong economy	Weak Economy
Do nothing	25	23	25
Sell the firm	45	0	45
Modernize the line	0	56	56

Step 3:

Since the minimum of all the maximum regret is $25 that is associated with the do nothing, so best alternative is do nothing as per Minimax criteria.

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Probability of strong economy = 30%

Probability of weak economy = 70%

Payoff for do nothing = .3*31 + .7*(-12) = $.9

Payoff for selling the firm = .3*11 + .7*11 = $11

Payoff for modernizing the line =.3*56 + .7*(-45) = -$14.7

The highest payoff is $11, so best alternative is selling the firm.