Expected savings

E$($M$1)=10*0\mathrm{.}3+20*0\mathrm{.}25+30*0\mathrm{.}45=21\mathrm{.}5$

E$($M$2)=22*0\mathrm{.}3+26*0\mathrm{.}25+26*0\mathrm{.}45=24\mathrm{.}8$

E$($M$3)=40*0\mathrm{.}3+30*0\mathrm{.}25+15*0\mathrm{.}45=26\mathrm{.}25$

the best policy based on the most probable future criteria is M$3$

Laplace ryke method

L$1$ L$2$ L$3$ Expected Payoff

M$1102030(10+20+30)/3=20$

M$2222626(22+26+26)/3=24\mathrm{.}67$

M$3403015(40+30+15)/3=28\mathrm{.}33$

M$3$ is best on this basis

Maximax rule

L$1$ L$2$ L$3$ maximum of row

M$110203030$

M$222262626$

M$340301540$

M$3$ has payoff $40$ s

Hurwicz rule

L$1$ L$2$ L$3$ max of row min of row P$=0\mathrm{.}2*$Max $+0\mathrm{.}8*$Min

M$110203030106+8=14$

M$2222626262222\mathrm{.}8$

M$3403015401520$

M$2$ is best policy by this rule