Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
13. Refer to the computer solution of Problem 12 in Figure 3.17. a. Identify the range of optimality for each objective function coefficient. 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? c. Identify the range of feasibility for the right-hand-side values. d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.

13. Refer to the computer solution of Problem 12 in Figure 3.17. a. Identify the range of optimality for each objective function coefficient. 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? c. Identify the range of feasibility for the right-hand-side values. d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%

I need question 13, question 12 is for background information 

12. Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respec- tively. The production requirements per unit are as follows: Number of Fans Manufacturing Time (hours) Number of Cooling Coils Economy Standard Deluxe 1 8 1 2 1 12 1 4 14 For the coming production period, the company has 200 fan motors, 320 cooling coils, and 2400 hours of manufacturing time available. How many economy models (E), stan- dard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E + 95S + 135D s.t. 1E + 1S + 1D< 200 Fan motors 1E + 2S + Cooling coils Manufacturing time 4D < 320 8E + 12S + 14D < 2400 E, S, D 0
Transcribed Image Text:12. Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respec- tively. The production requirements per unit are as follows: Number of Fans Manufacturing Time (hours) Number of Cooling Coils Economy Standard Deluxe 1 8 1 2 1 12 1 4 14 For the coming production period, the company has 200 fan motors, 320 cooling coils, and 2400 hours of manufacturing time available. How many economy models (E), stan- dard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E + 95S + 135D s.t. 1E + 1S + 1D< 200 Fan motors 1E + 2S + Cooling coils Manufacturing time 4D < 320 8E + 12S + 14D < 2400 E, S, D 0
FIGURE 3.17 THE SOLUTION FOR THE QUALITY AIR CONDITIONING PROBLEM 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 Coefficient Allowable Allowable Variable Increase Decrease E 63.00000 12.00000 15.50000 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 The computer solution is shown in Figure 3.17. a. What is the optimal solution, and what is the value of the objective function? b. Which constraints are binding? c. Which constraint shows extra capacity? How much? d. If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change? Use the information in Figure 3.17 to answer this question. 13. Refer to the computer solution of Problem 12 in Figure 3.17. a. Identify the range of optimality for each objective function coefficient. 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? c. Identify the range of feasibility for the right-hand-side values. d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.
Transcribed Image Text:FIGURE 3.17 THE SOLUTION FOR THE QUALITY AIR CONDITIONING PROBLEM 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 Coefficient Allowable Allowable Variable Increase Decrease E 63.00000 12.00000 15.50000 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 The computer solution is shown in Figure 3.17. a. What is the optimal solution, and what is the value of the objective function? b. Which constraints are binding? c. Which constraint shows extra capacity? How much? d. If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change? Use the information in Figure 3.17 to answer this question. 13. Refer to the computer solution of Problem 12 in Figure 3.17. a. Identify the range of optimality for each objective function coefficient. 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? c. Identify the range of feasibility for the right-hand-side values. d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS