Mgmt 650
Brittany Asay
MGMT 650
Chapters 3 & 4 Homework Problems
May 14, 2013
Chapter 3:
13. Refer to the computer solution of Problem 12 in Figure 3.17.
a. Identify the range of optimality for each objective function coefficient. E: 47.5-75 S: 87-126 D: there is no lower limit until 159
b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? The optimal solution is unchanged, but the profit increases.
c. Identify the range of feasibility for the right-hand-side values:
Constraint 1: 160-180
Constraint 2: 200-400
Constraint 3: 2080 to no limit
d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain. Yes, if the number of fan motors available for production increased by 100, the dual value would change. This is because 100 > 80.
Optimal Objective Value = 16440.00000
Variable Value Reduced Cost
-------------- --------------- -----------------
E 80.00000 0.00000
S 120.00000 0.00000
D 0.00000 -24.00000
Constraint Slack/Surplus Dual Value
-------------- --------------- -----------------
1 0.00000 31.00000
2 0.00000 32.00000
3 320.00000 0.00000
Objective Allowable Allowable
Variable Coefficient Increase Decrease
---------- ------------ ---------- ----------
E 63.00000 12.00000 15.50000
S 95.00000 31.00000 8.00000
D 135.00000 24.00000 Infinite
RHS Allowable Allowable
Constraint Value Increase Decrease
---------- ------------ ---------- ----------
1 200.00000 80.00000 40.00000
2 320.00000 80.00000 120.00000
3 2400.00000 Infinite 320.00000
3.21 Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:
MGMT 650
Chapters 3 & 4 Homework Problems
May 14, 2013
Chapter 3:
13. Refer to the computer solution of Problem 12 in Figure 3.17.
a. Identify the range of optimality for each objective function coefficient. E: 47.5-75 S: 87-126 D: there is no lower limit until 159
b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? The optimal solution is unchanged, but the profit increases.
c. Identify the range of feasibility for the right-hand-side values:
Constraint 1: 160-180
Constraint 2: 200-400
Constraint 3: 2080 to no limit
d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain. Yes, if the number of fan motors available for production increased by 100, the dual value would change. This is because 100 > 80.
Optimal Objective Value = 16440.00000
Variable Value Reduced Cost
-------------- --------------- -----------------
E 80.00000 0.00000
S 120.00000 0.00000
D 0.00000 -24.00000
Constraint Slack/Surplus Dual Value
-------------- --------------- -----------------
1 0.00000 31.00000
2 0.00000 32.00000
3 320.00000 0.00000
Objective Allowable Allowable
Variable Coefficient Increase Decrease
---------- ------------ ---------- ----------
E 63.00000 12.00000 15.50000
S 95.00000 31.00000 8.00000
D 135.00000 24.00000 Infinite
RHS Allowable Allowable
Constraint Value Increase Decrease
---------- ------------ ---------- ----------
1 200.00000 80.00000 40.00000
2 320.00000 80.00000 120.00000
3 2400.00000 Infinite 320.00000
3.21 Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: