Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A linear programming computer package is needed. Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here. Min s.t. Hours required to complete all the oak cabinets Hours required to complete all the cherry cabinets Hours available Cost per hour oak hours available 1 cherry hours available 2 hours available 3 Cabinetmaker 1 01, 02, 03, C1, C2, C3 ≥ 0 50 60 00000 40 $36 Cabinetmaker 2 42 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80 %, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. 48 (a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. (Let 01 = percentage of oak cabinets assigned to cabinetmaker 1, 02 = percentage of oak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker 3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.) 30 $42 Cabinetmaker 3 30 35 35 $55

A linear programming computer package is needed. Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here. Min s.t. Hours required to complete all the oak cabinets Hours required to complete all the cherry cabinets Hours available Cost per hour oak hours available 1 cherry hours available 2 hours available 3 Cabinetmaker 1 01, 02, 03, C1, C2, C3 ≥ 0 50 60 00000 40 $36 Cabinetmaker 2 42 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80 %, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. 48 (a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. (Let 01 = percentage of oak cabinets assigned to cabinetmaker 1, 02 = percentage of oak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker 3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.) 30 $42 Cabinetmaker 3 30 35 35 $55

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
A linear programming computer package is needed. Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here. Min s.t. Hours required to complete all the oak cabinets Hours required to complete all the cherry cabinets Hours available Cost per hour hours available 1 oak hours available 2 cherry hours available 3 Cabinetmaker 1 01, 02, 03, C1, C2, C3 20 50 60 00000 40 $36 Cabinetmaker 2 42 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. 48 (a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. (Let 01 = percentage of oak cabinets assigned to cabinetmaker 1, 02 = percentage of oak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker 3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.) 30 $42 Cabinetmaker 3 30 35 35 $55
Transcribed Image Text:A linear programming computer package is needed. Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here. Min s.t. Hours required to complete all the oak cabinets Hours required to complete all the cherry cabinets Hours available Cost per hour hours available 1 oak hours available 2 cherry hours available 3 Cabinetmaker 1 01, 02, 03, C1, C2, C3 20 50 60 00000 40 $36 Cabinetmaker 2 42 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. 48 (a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. (Let 01 = percentage of oak cabinets assigned to cabinetmaker 1, 02 = percentage of oak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker 3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.) 30 $42 Cabinetmaker 3 30 35 35 $55
(b) Solve the model formulated in part (a). What percentage of the oak cabinets and what percentage of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost (in $) of completing both projects? (Round your percentage values to one decimal place.) 01 02 03 C1 C2 C3 total cost $ % % % % % % (c) If Cabinetmaker 1 has additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $5 per hour. O Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $-1.75 per hour. No, cabinetmaker 1 has a slack of 37.5 hours, so increasing cabinetmaker 1's time will not reduce costs. O No, cabinetmaker 1 has a slack of 26.458 hours, so increasing cabinetmaker 1's time will not reduce costs. (d) If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. O Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $5 per hour. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $-1.75 per hour. O No, cabinetmaker 2 has a slack of 37.5 hours, so increasing cabinetmaker 2's time will not reduce costs. O No, cabinetmaker 2 has a slack of 26.458 hours, so increasing cabinetmaker 2's time will not reduce costs. (e) Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? Explain. The new objective function coefficients for 02 and C2 are and , respectively. The optimal solution does not change ✔ and has a value of $
Transcribed Image Text:(b) Solve the model formulated in part (a). What percentage of the oak cabinets and what percentage of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost (in $) of completing both projects? (Round your percentage values to one decimal place.) 01 02 03 C1 C2 C3 total cost $ % % % % % % (c) If Cabinetmaker 1 has additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $5 per hour. O Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $-1.75 per hour. No, cabinetmaker 1 has a slack of 37.5 hours, so increasing cabinetmaker 1's time will not reduce costs. O No, cabinetmaker 1 has a slack of 26.458 hours, so increasing cabinetmaker 1's time will not reduce costs. (d) If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. O Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $5 per hour. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $-1.75 per hour. O No, cabinetmaker 2 has a slack of 37.5 hours, so increasing cabinetmaker 2's time will not reduce costs. O No, cabinetmaker 2 has a slack of 26.458 hours, so increasing cabinetmaker 2's time will not reduce costs. (e) Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? Explain. The new objective function coefficients for 02 and C2 are and , respectively. The optimal solution does not change ✔ and has a value of $
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 17 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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