This preview shows pages 1–3. Sign up to view the full content.
Question 1
(45 marks)
Fred Johanasson
(a) The 3 decisions facing Fred are:
How many kilograms of corn to include in the daily diet
How many kilograms of tankage to include in the daily diet
3 marks
How many kilograms of alfalfa to include in the daily diet
(b)The costs of all three ingredients
are relevant costs.
1 mark
This is because the costs of all 3 ingredieints have been included in the target cel
1 mark
c) See
attached Model 1
13 marks
(d)
The total weight to feed each pig per day is
3.57 kg
(1.14 + 0.00 + 2.43)
2 marks
(e)
$1.06
(3.48  2.42)
2 marks
Note: This is determeined by rerunning the model
with C = 1, T = 2 and A = 2
(f)
The 20%to 35% corn constraint
HAS NO EFFECT
on the value of the target cell.
1 mark
Because these constraints are
NON_BINDING
1 mark
(g)
The optimal soluion is:
Corn =
1.14 kg
Tankage =
0.00 kg
3 mark
Alfalfa =
2.43 kg
(h)
For each reduction in the carbohydrate level
not required
the Target Cell will go down by $0.007714286
New
TOTAL COST: $2.30
(.007714286 x 15)
3 marks
(i)
See Model 1
attached
2 marks
See Sensitivity Report1 attached
2 marks
Part (j)
(11 marks)
Let C = # kilograms of corn in the daily diet
Let T = # kilograms of Tankage in the daily diet
3 marks
Let A = # kilograms of Alfalfa in the daily diet
Minimize
0.84C + 0.72T + 0.60A
1 mark
subject to:
90C + 20T + 40A >=
200
30C + 80T + 60A >=
180
10C + 20T + 60A >=
150
C <= 0.35(C +T+A)
7 marks
C >= 0.20(C +T + A)
(1 mark each)
A + T
>=
0.60 ( C + T + A)
C,T,A >=
0
1 mark for the
answer; 1 mark
for showing the
calculations to
determine that
number
1 mark for the
answer; 2
marks for
showing the
calculation
Question 1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentQuestion #1
Fred Jonasson Farms (Parts c and d)
Input Items
Nutritional
Each Kilogram of
Model
Model
Ingredient
Corn
Tankage
Alfalfa
Output
Requirement
Carbohydrates
90
20
40
200
≥
200
units
Proteins
30
80
60
180
≥
180
units
Vitamins
10
20
60
157
≥
150
units
Total Cost
Unit Cost
0.84
$
0.72
$
0.60
$
$2.42
Solution
Action Plan
Corn
Tankage
Alfalfa
Total Weight
# of kilograms of
1.14
0.00
2.43
3.57
Additional Constraints
(Blending Constraints)
Model
Model
Output
Requirement
Corn
1.14
<=
1.25
kg
Corn must be at most
0.35
of Total Weight
Corn
1.14
>=
0.71
kg
Corn must be at least
0.20
of Total Weight
Tankage + Alfalfa
2.43
>=
2.14
kg
Tankage + Alfalfa must be at least
0.60
of Total Weight
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '09
 BRIANOGRAM

Click to edit the document details