1)
1M1-1MS1=130
Month 1 Demand Men’s bikes
2)
1W1-1WS1=95
Month 1 Demand Women’s bikes
3)
1M2+1MS1-1MS2=200
Month 2 Demand Men’s bikes
4)
1W2+1WS1-1WS2=150
Month 2 Demand Women’s bikes
5)
1MS2>25
Inventory requirement Men’s
6)
1WS2>25
Inventory requirement Women’s
7)
3.5M1+2.6W1>900
Month 1 labor Minimum
8)
3.5M1+2.6W1<1100
Month 1 labor Maximum
9)
3.5M1+2.6W1-3.5M2-2.6W2<100
Month 2 labor
10)
-3.5M1-2.6W1+3.5M2+2.6W2<100
Month 2 labor
Objective Function Value =
67156.029
Variable
Value
Reduced Costs
M1
192.929
0.000
W1
95.000
0.000
M2
162.071
0.000
W2
175.000
0.000
MS1
62.929
0.000
WS1
0.000
0.017
MS2
25.000
0.000
WS2
25.000
0.000
Constraint
Slack/Surplus
Dual Prices
1
0.000
-118.800
2
0.000
-89.109
3
0.000
-121.200
4
0.000
-90.891
5
0.000
-123.600
6
0.000
-92.691
7
22.250
0.000
8
177.750
0.000
9
200.000
0.000
10
0.000
0.343
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
Current Value
Upper Limit
M1
117.600
120.000
120.023
W1
89.983
90.000
No Upper Limit
M2
119.977
120.000
122.400
W2
-2.691
90.000
90.017
MS1
0.000
2.400
2.423
WS1
1.783
1.800
No Upper Limit
MS2
-121.200
2.400
No Upper Limit
WS2
-90.891
1.800
No Upper Limit

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5
8. As part of a settlement for a class action lawsuit, Cheney-Burton must provide sufficient cash
to pay out 750 thousand dollars over the next five years (including the current year).
Annual
payments, as outlined by the judge in the case, must be made at the beginning of each year.
The
initial payment will be made in cash with the payments over the next four years made from
interest on two types of Government Securities (purchased at the beginning of year one only) and
one year risk-free securities.
Funds not invested in Government securities will be placed in one
year risk-free security investments.
Interest is paid annually for all investment alternatives.
The
current price of both Government Securities is $1,000 (par value = $1,000). The LP solution is
provided below (each question is worth two points)
8a. How much cash does Cheney-Burton need to provide at the beginning of the first year in
order to cover the $750 payments due over the five year period?
____________
8b. If the payment required at the beginning of the third year was $190 thousand, would the
binding constraint change?
Provide numerical support for your answer.
8c. During which year will the first Government Security mature?
________
How many years does it take for the first Government Security to mature? ____________\
8d. Should Cheney-Burton be willing to pay $6 thousand now to reduce the payment at the
beginning of year four by $10 thousand?
Provide numerical support for your answer.
8e.
How much extra
should Cheney-Burton be willing to pay now (the first year; 100,000 + ? -
increases the amount the litigant gets now by how much) to reduce the beginning payment of
year five from $200 (thousand) to $180 (thousand)?

6
OPTIMAL SOLUTION
Objective Function Value =
652.451
Variable
Value
Reduced Costs
--------------
---------------
------------------
GS1
274.643
0.000
GS2
186.916
0.000
S1
90.893
0.000
S2
0.000
0.018
S3
154.206
0.000
S4
0.000
0.051
F
652.451
0.000
Constraint
Slack/Surplus
Dual Prices
--------------
---------------
------------------
1
0.000
-1.000
2
0.000
-0.952
3
0.000
-0.889
4
0.000
-0.847
5
0.000
-0.759
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
Current Value
Upper Limit
------------
---------------
---------------
---------------
GS1
-0.049
0.000
0.019
GS2
No Lower Limit
0.000
0.051
S1
-0.018
0.000
No Upper Limit
S2
-0.018
0.000
No Upper Limit
S3
-0.050
0.000
No Upper Limit
S4
-0.051
0.000
No Upper Limit
F
0.000
1.000
No Upper Limit
RIGHT HAND SIDE RANGES
Constraint
Lower Limit
Current Value
Upper Limit
------------
---------------
---------------
---------------
1
-552.451
100.000
No Upper Limit
2
29.563
125.000
No Upper Limit
3
-141.121
150.000
183.059
4