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. 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: Laeon Mortis

Table $2$

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 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.

c$)$ If he uses the equally likely criterion, which kind of dwellings will he choose to build? Show your supporting calculations.

d$)$ Which dwelling type is BEST in accordance with a decision criterion of minimax regret? Show your supporting calculations.