Transcript Assignment 2 - University of Waterloo

Assignment 2
Question 7
Farmer Leary
1
Farmer Leary
• Farmer Leander grows wheat and corn on his 45-acre farm in
Saskatoon. He can sell at most 140 bushels of wheat and 120
bushels of corn. Each planted acre yields either 5 bushels of wheat
or 4 bushels of corn. Wheat sells for $30 per bushel, and corn sells
for $50 per bushel. Six hours of labour are needed to harvest an
acre of wheat, and ten hours are needed to harvest an acre of corn.
Up to 350 hours of labour can be purchased at $10 per hour. Let
– A1 = acres planted with wheat
– A2 = acres planted with corn
– L = hours of labour that are purchased
• Farmer Leander maximizes his profits by solving the LP problem
stated in the LINDO output below.
• Answer the following questions according to this LINDO output (do
not resolve it each time). Justify your answers for each.
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Farmer Leary
MAX
SUBJECT TO
2)
3)
4)
5)
6)
END
150 A1 + 200 A2 - 10 L
RANGES IN WHICH THE BASIS IS UNCHANGED:
A1 + A2
<= 45
6 A1 + 10 A2 - L <= 0
L <= 350
5 A1
<= 140
4 A2 <= 120
LP OPTIMUM FOUND AT STEP
OBJ COEFFICIENT RANGES
VARIABLE
CURRENT
ALLOWABLE
COEF
INCREASE
A1 150.000000
10.000000
A2 200.000000
50.000000
L -10.000000
INFINITY
1
ROW
OBJECTIVE FUNCTION VALUE
1)
4250.000
VARIABLE
VALUE
A1
25.000000
A2
20.000000
L
350.000000
ROW
2)
3)
4)
5)
6)
2
3
4
5
6
SLACK OR SURPLUS
0.000000
0.000000
0.000000
15.000000
40.000000
REDUCED COST
0.000000
0.000000
0.000000
RIGHTHAND SIDE RANGES
CURRENT
ALLOWABLE
RHS
INCREASE
45.000000
1.200000
0.000000
40.000000
350.000000
40.000000
140.000000
INFINITY
120.000000
INFINITY
ALLOWABLE
DECREASE
30.000000
10.000000
2.500000
ALLOWABLE
DECREASE
6.666667
12.000000
12.000000
15.000000
40.000000
DUAL PRICES
75.000000
12.500000
2.500000
0.000000
0.000000
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