Wivco produces Product 1 and Product 2 by processing raw material. Up to 90 lbs
ID: 3383359 • Letter: W
Question
Wivco produces Product 1 and Product 2 by processing raw material. Up to 90 lbs of raw material may be purchased at a cost of $10/lb. One pound of raw material can be used to produce either 1 lb of product 1 or 0.33 lb of product 2. Using a pound of raw material to produce product 1 requires 2 hours of labor or 3 hours to produce 0.33 lb of product 2. A total of 200 hours of labor is available. At most 40 lbs of Product 2 can be sold. Product 1 sells for $13/lb and Product 2 for $40/lb.
a) Formulate a Linear Program (LP) that maximizes Wivco’s profit.
b) Solve the LP using LINDO.
Explanation / Answer
. Let
RM = pounds of raw material processed
P1 = pounds of raw material used to produce product 1
P2 = pounds of raw material used to produce product 2
To maximize profit, Wivco should solve the following LP:
Max z =13P1 + 40(0.33)P2 – 10RM
Such that,
RMP1 + P2
2P1 + 3P2200
RM90
0.33P240
P1, P2, RM0
b) Solve the LP using LINDO.
Using LINDO to solve the LP.
LINDO Output for Wivco
MAX
13 P1 + 13.2 P2 - 10 RM
SUBJECT TO
2) - P1 - P2 + RM >= 0
3)
2 P1 + 3 P2 <=
200
4)
RM <=
90
5)
0.33 P2 <=
40
END
LP OPTIMUM FOUND
AT STEP
3
OBJECTIVE FUNCTION VALUE
1)
274.000000
VARIABLE
VALUE
REDUCED COST
P1
70.000000
0.000000
P2
20.000000
0.000000
RM
90.000000
0.000000
ROW
SLACK OR SURPLUS
DUAL PRICES
2)
0.000000
-12.600000
3)
0.000000
0.200000
4)
0.000000
2.600000
5)
33.400002
0.000000
NO. ITERATIONS=
3
RANGES IN WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES
VARIABLE
CURRENT
ALLOWABLE
ALLOWABLE
COEF
INCREASE
DECREASE
P1
13.000000
0.200000
0.866667
P2
13.200000
1.300000
0.200000
RM
-10.000000
INFINITY
2.600000
RIGHTHAND SIDE RANGES
ROW
CURRENT
ALLOWABLE
ALLOWABLE
RHS
INCREASE
DECREASE
2
0.000000
23.333334
10.000000
3
200.000000
70.000000
20.000000
4
90.000000
10.000000
23.333334
5
40.000000
INFINITY
33.400002
MAX
13 P1 + 13.2 P2 - 10 RM
SUBJECT TO
2) - P1 - P2 + RM >= 0
3)
2 P1 + 3 P2 <=
200
4)
RM <=
90
5)
0.33 P2 <=
40
END
LP OPTIMUM FOUND
AT STEP
3
OBJECTIVE FUNCTION VALUE
1)
274.000000
VARIABLE
VALUE
REDUCED COST
P1
70.000000
0.000000
P2
20.000000
0.000000
RM
90.000000
0.000000
ROW
SLACK OR SURPLUS
DUAL PRICES
2)
0.000000
-12.600000
3)
0.000000
0.200000
4)
0.000000
2.600000
5)
33.400002
0.000000
NO. ITERATIONS=
3
RANGES IN WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES
VARIABLE
CURRENT
ALLOWABLE
ALLOWABLE
COEF
INCREASE
DECREASE
P1
13.000000
0.200000
0.866667
P2
13.200000
1.300000
0.200000
RM
-10.000000
INFINITY
2.600000
RIGHTHAND SIDE RANGES
ROW
CURRENT
ALLOWABLE
ALLOWABLE
RHS
INCREASE
DECREASE
2
0.000000
23.333334
10.000000
3
200.000000
70.000000
20.000000
4
90.000000
10.000000
23.333334
5
40.000000
INFINITY
33.400002
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