BUS 104 Solution of Homework 3
Solution to Homework #3
4.
a.
Y
10
8
6
Optimal Solution
X = 2.5, Y = 2.5
4
8 (2
2
.5)
+1
2 (2
2
.5)
=5
0
4
X
6
8
10
b. The value of the optimal solution to the revised problem is 8(2.5) + 12(2.5) = 50.
Compared to the original problem, the value of the optimal solution has increased by 50 48 = 2. Thus, the dual value is 2.
c. The right-hand side range for constraint 1 is 5 to 11. As long as the right-hand side stays within this range, the dual value of 2 is applicable. Since increasing the right-hand side does not improve the value of the optimal solution, decreasing the right-hand side of constraint 1 would b desirable.
d. As long as the right-hand side of constraint 2 is between 9 and 18, a unit increase in the right-hand side will cause the value of the optimal solution to increase by 3.
5.
a. Regular Glove = 500
Catcher’s Mitt = 150
Value = 3700
b. The finishing and packaging and shipping constraints are binding.
c. Cutting and Sewing = 0
Finishing = 3
Packaging and Shipping = 28
Additional finishing time is worth $3 per unit and additional packaging and shipping time is worth
$28 per unit.
d. In the packaging and shipping department. Each additional hour is worth $28.
6.
a.
Variable
Objective Coefficient
Range
Regular Glove
4 to 12
Catcher’s Mitt
3.33 to 10
b. As long as the profit contribution for the regular glove is between $4.00 and $12.00, the current solution is optimal.
As long as the profit contribution for the catcher's mitt stays between $3.33 and $10.00, the current solution is optimal.
The optimal solution is not sensitive to small changes in the profit contributions for the gloves. c. The dual values for the resources are applicable over the following ranges:
Constraint
Right-Hand-Side
Range
Cutting and Sewing
725 to No Upper Limit
Finishing
133.33 to 400
Packaging
75 to 135
d. Amount of increase = (28) (20) = $560
12. a. E = 80, S = 120, D = 0
Profit = $16,440
b. Fan motors and cooling coils
c.
4.
a.
Y
10
8
6
Optimal Solution
X = 2.5, Y = 2.5
4
8 (2
2
.5)
+1
2 (2
2
.5)
=5
0
4
X
6
8
10
b. The value of the optimal solution to the revised problem is 8(2.5) + 12(2.5) = 50.
Compared to the original problem, the value of the optimal solution has increased by 50 48 = 2. Thus, the dual value is 2.
c. The right-hand side range for constraint 1 is 5 to 11. As long as the right-hand side stays within this range, the dual value of 2 is applicable. Since increasing the right-hand side does not improve the value of the optimal solution, decreasing the right-hand side of constraint 1 would b desirable.
d. As long as the right-hand side of constraint 2 is between 9 and 18, a unit increase in the right-hand side will cause the value of the optimal solution to increase by 3.
5.
a. Regular Glove = 500
Catcher’s Mitt = 150
Value = 3700
b. The finishing and packaging and shipping constraints are binding.
c. Cutting and Sewing = 0
Finishing = 3
Packaging and Shipping = 28
Additional finishing time is worth $3 per unit and additional packaging and shipping time is worth
$28 per unit.
d. In the packaging and shipping department. Each additional hour is worth $28.
6.
a.
Variable
Objective Coefficient
Range
Regular Glove
4 to 12
Catcher’s Mitt
3.33 to 10
b. As long as the profit contribution for the regular glove is between $4.00 and $12.00, the current solution is optimal.
As long as the profit contribution for the catcher's mitt stays between $3.33 and $10.00, the current solution is optimal.
The optimal solution is not sensitive to small changes in the profit contributions for the gloves. c. The dual values for the resources are applicable over the following ranges:
Constraint
Right-Hand-Side
Range
Cutting and Sewing
725 to No Upper Limit
Finishing
133.33 to 400
Packaging
75 to 135
d. Amount of increase = (28) (20) = $560
12. a. E = 80, S = 120, D = 0
Profit = $16,440
b. Fan motors and cooling coils
c.