The construction manager for Acme Construction, Inc must decide whether to build single family homes, apartments, or condominiums. This is not a product-mix problem, but an all-or-nothing decision

Question

He will hire workers and rent equipment appropriate for one action only. He estimates annual profits (in thousands of dollars) will vary with population trends as follows:
Dwelling type Population steady Population grows slowly Population grows rapidly
Single family $100 $90 $70
Apartments 50 170 90
Condominiums -20 100 220

a. If he uses the maximin criterion, which type of dwellings will he choose to build? Show your supporting calculations.
b. If he uses the equally likely criterion, which kind of dwellings will he choose to build? Show your supporting calculations.
c. If the construction manager were an optimist, what criterion would he choose? What would be the choice of dwelling for that criterion? Show your supporting calculations.

Answer 1

(a) The pessimistic maximin criterion assumes the worst state of nature will occur and selects the action associated with the best of these worst outcomes. For this problem, the "worsts" for each action are Single family = $70, Apartments = $50, and Condominiums = -20. The best of the worsts is $70, so the manager should choose to build single family homes.
(b) The equally likely criterion calculates the simple average of each action; the results are Single family = $86.7, Apartments = $103.3, and Condominiums = $100. The manager should select the action associated with the largest of these values, and build apartments.
(c) The optimistic criterion is maximax, which assumes that the best outcome will occur for each action. The best outcomes are Single family = $100, Apartments = $170, and Condominiums = $220. The manager chooses the action associated with the best of the bests, or Condominiums.