1. John Humber is a farmer who intends to sign a contract to provide a cannery with his entire
crop. John must choose to produce one of the following vegetables: tomatoes, beets, or
asparagus. The yields of these vegetables will be affected by the weather to varying degrees.
The following table indicates the approximate profits (in $ thousands) depending on the
weather: dry, moderate, or damp.
Weather
Decision Alternatives
Dry Moderate Damp
Tomatoes 40 80 50
Beets 50 60 70
Asparagus 60 50 30
Determine the best decision using the following decision criteria.
a. (2 marks) Maximax
Max C 80 , to , 60 ) = to
↳ tomatoes
/
b. (2 marks) Maximin max in min
Maximin ( 40, 50 , 30) = 3050
↳ beets
asparagines
c. (2 marks) Equally likely (Laplace) criterion
tomato = 56.67
beets = 60
46.67
asparagus
=
( 5h 67 bro , 46.67 ) = 60
Max . ,
↳ beets
/
, 2
d. (3 marks) Criterion of realism (Hurwicz criterion). Use an value of 0.3.
tomatoes = 0 . 3 x 80 t 0.7×40 = 52
beets =
0.3 x 70 t 0.7×50 = 56
0.3 x 60 t 0.7 × 30 = 39
asparagus =
Max C 52,56 397=56 ,
→ beets
/
e. (3 marks) Opportunity Loss Criterion.
dhy moderate damp
80-80=0 70 -
50=20
tomatoes 60 -
40=20
beets 60 -
50 = 10 80 -
60=20 70 -
70 = 0
60 60=0 80 -
50 = 30 70 -
30=40
asparagus
-
tomatoes
20
-
select ruin
beets do
- Value
40
asparagus
beets
→ tomatoes
✓
2
crop. John must choose to produce one of the following vegetables: tomatoes, beets, or
asparagus. The yields of these vegetables will be affected by the weather to varying degrees.
The following table indicates the approximate profits (in $ thousands) depending on the
weather: dry, moderate, or damp.
Weather
Decision Alternatives
Dry Moderate Damp
Tomatoes 40 80 50
Beets 50 60 70
Asparagus 60 50 30
Determine the best decision using the following decision criteria.
a. (2 marks) Maximax
Max C 80 , to , 60 ) = to
↳ tomatoes
/
b. (2 marks) Maximin max in min
Maximin ( 40, 50 , 30) = 3050
↳ beets
asparagines
c. (2 marks) Equally likely (Laplace) criterion
tomato = 56.67
beets = 60
46.67
asparagus
=
( 5h 67 bro , 46.67 ) = 60
Max . ,
↳ beets
/
, 2
d. (3 marks) Criterion of realism (Hurwicz criterion). Use an value of 0.3.
tomatoes = 0 . 3 x 80 t 0.7×40 = 52
beets =
0.3 x 70 t 0.7×50 = 56
0.3 x 60 t 0.7 × 30 = 39
asparagus =
Max C 52,56 397=56 ,
→ beets
/
e. (3 marks) Opportunity Loss Criterion.
dhy moderate damp
80-80=0 70 -
50=20
tomatoes 60 -
40=20
beets 60 -
50 = 10 80 -
60=20 70 -
70 = 0
60 60=0 80 -
50 = 30 70 -
30=40
asparagus
-
tomatoes
20
-
select ruin
beets do
- Value
40
asparagus
beets
→ tomatoes
✓
2
