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Assignment Problem 1
a) i. For City 1 construct the payoff matrix to General Custard.
General Peabody
Gen. Custard

0
1
2
3

0
0
-1
-1
-1

1
1
0
-2
-2

2
1
2
0
-3

3
1
2
3
0

4
1
2
3
4 ii. For City 2 construct the payoff matrix to General Custard.
General Peabody
Gen. Custard

3
2
1
0

4
4
3
2
1

3
0
3
2
1

2
-3
0
2
1

1
-2
-2
0
1

0
-1
-1
-1
0 iii. Let (x,y) where x is the number of regiments in City 1 and y is the number of regiments in City 2. Now use your answers to parts i. and ii. to obtain the overall payoff matrix to General Custard.
General Peabody
Gen. Custard

(0,3) (1,2)
(2,1)
(3,0)

(0,4)
4
2
1
0

(1,3)
1
3
0
-1

(2,2)
-2
2
2
-2

(3,1)
-1
0
3
1

(4,0)
0
1
2
4
(b) Write down General Custard’s LP. Solve it using Excel Solver. After Solver updates the decision variables’ values, take a screen-shot of your spread sheet and paste it into your assignment, to show how you set it up and what the optimal values are. Also take a screen-shot of the Answer Report and paste it into your assignment. Report your solution in your own words.
Solution:
Let X1 = P (the 1 regiment in City 1 General Custard choose, and 3 regiments in City 2)
X2= P (the 2 regiments in City 1 General Custard choose, 2 regiments in City2)
X3 = P (the 3 regiments in City 1General Custard choose, 1 regiment in City2)
X4 = P (the 4 regiments in City 1 General Custard choose, no regiment in City2)
X0 = P (no regiment in City 1 General Custard choose, 4 regiments in City 2)
Max z=v
Subject to v4X0+X1-2X2-X3+0X4 V≤2X0+3X1+2X2+0X3+X4
V≤1X0+0X1+2X2+3X3+2X4
V≤0X0-X1-2X2+X3+4X4
X1+X2+X3+X4+X0=1
X1, X2, X3, X4, X0 ≥0, V IS UNRESTRICTED IN SIGN

So the X1 = P (the 1 regiment in City 1 General Custard choose, and 3 regiments in City 2)=0.15
X2= P (the 2 regiments in City 1 General Custard choose, 2 regiments in City2)=0
X3 = P (the 3 regiments in City 1General Custard choose, 1 regiment in City2)=0
X4 = P (the 4 regiments in City 1 General Custard choose, no regiment in City2)=0.46
X0 = P (no regiment in City 1 General Custard choose, 4 regiments in City 2)=0.38

(c) Write down General Peabody’s LP. Solve it using Excel Solver. After Solver updates the decision variables’ values, take a screen-shot of your spread sheet and paste it into your assignment, to show how you set it up and what the optimal values are. Also take a screen-shot of the Answer Report and paste it into your assignment. Report your solution in your own words.
LET
Y1= P (1 regiment in City 2 General Peabody choose, 2 regiments in City2)
Y2= P (2 regiments in City 2 General Peabody choose, 1 regiment in City2)
Y3= P (3 regiments in City 2 General Peabody choose, no regiment in City2)
Y0= P (no regiment in City 2 General Peabody choose, and 3 regiments in City 2)
Min Z=W
W≥4Y0+2Y2+Y3+0Y4
W≥1Y0+3Y2+0Y3-1Y4
W≥-2Y0+2Y2+2Y3-2Y4
W≥0Y0+1Y2+2Y3+4Y4