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Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags. Par Inc.’s distributor is enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc., produces over the next three months. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations:   Cutting and dyeing the material Sewing Finishing (inserting umbrella holder, club separators, etc.) Inspection and packaging

Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags. Par Inc.’s distributor is enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc., produces over the next three months. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations:   Cutting and dyeing the material Sewing Finishing (inserting umbrella holder, club separators, etc.) Inspection and packaging

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags. Par Inc.’s distributor is enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc., produces over the next three months.

After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations:

 

  1. Cutting and dyeing the material
  2. Sewing
  3. Finishing (inserting umbrella holder, club separators, etc.)
  4. Inspection and packaging
Problem 2-15 Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags. Par Inc.'s distributor is enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc., produces over the next three months. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations: a. Cutting and dyeing the material b. Sewing c. Finishing (inserting umbrella holder, club separators, etc.) d. Inspection and packaging The director of manufacturing analyzed each of the operations and concluded that if the company produces a medium-priced standard model, each bag will require 7/10 hour in the cutting and dyeing department, 1/2 hour in the sewing department, 1 hour in the finishing department, and 1/10 hour in the inspection and packaging department. The more expensive deluxe model will require 1 hour for cutting and dyeing, 5/6 hour for sewing, 2/3 hour for finishing, and 1/4 hour for inspection and packaging. This production information is summarized in the following table: Production Time (hours) Department Standard Bag Deluxe Bag Cutting and Dyeing 7/10 1 Sewing 1/2 5/6 Finishing 1 2/3 Inspection and Packaging 1/10 1/4 Par Inc.'s production is constrained by a limited number of hours available in each department. After studying departmental workload projections, the director of manufacturing estimates that 630 hours for cutting and dyeing, 600 hours for sewing, 708 hours for finishing, and 135 hours for inspection and packaging will be available for the production of golf bags during the next three months. The accounting department analyzed the production data, assigned all relevant variable costs, and arrived at prices for both bags that will result in a profit contribution of $10 for every standard bag and $9 for every deluxe bag produced. Let us now develop a mathematical model of the Par, Inc., problem that can be used to determine the number of standard bags and the number of deluxe bags to produce in order to maximize total profit contribution. For each of the following independent situations, select the correct graph which shows the optimal solution and the total profit contribution: b. A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.) a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag. (i) AD (ii) AD 800- 800- (i) AD (ii) AD 800- 800- Optimalgolution (0, 720) Z= 12960 700- 700- 700- 700- 600- 600- 600- 600- 500- 500- 500- 500- 400- 400- Optimal solution (300, 420) Z= 10560 400- 400- 300- 300- Optimal solution (540, 252) Z- 13068 300- 300- 200- 200- 200- Optimal solution (708, 0) Z- 14160 100 200 30 400 500 600 700 200- 100- 100- 100- 100- 0- 100 200 300 400 500 600 700 100 20 300 400 50 600 700 100 200 300 400 500 600 700 (iii) B00 AD (iv) AD 800- (ii) AD AD 800- 700- 700- Optimalçolution (0, 720) Z= 12960 700- 700- 60- 600- 600- 600- 500- 500- 500- 500- 400- 400- Optimal solution (300, 420) Z= 10560 400- 400- 300 300- Optimal solution (540, 252) Z- 13068 300- 300- 200- 200- 200- 200- Optimal solution (708, 0) z- 14160 100 200 300 400 số0 600 100- 100- 100- 100- 100 200 300 400 500 60o 700 700 0- 100 200 300 400 500 600 700 100 200 300 400 500 600 700 c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A + 9B is the appropriate objective function.) (i) AD (ii) AD 800- 800- 700- 700- 600- 600- 500- 500- 400- 400- 300- 300- Optimal solution (540, 252) Z- 9068 Optimal solution (540, 252) Z-7768 200- 200- 100- 100- 100 200 300 400 s00 6do 70 100 200 30 400 500 600 70 (ii) AD (iv) AD 800- 800- 700- 700- 600- 600- 500- 500- Optimal solutio (300, 420) Z- 6780 400- 400- 300- 300- Optimal solution (540, 252) Z- 7768 200- 200- 100- 100- 100 200 300 400 500 600 100 200 300 400 500 600 700
Transcribed Image Text:Problem 2-15 Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags. Par Inc.'s distributor is enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc., produces over the next three months. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations: a. Cutting and dyeing the material b. Sewing c. Finishing (inserting umbrella holder, club separators, etc.) d. Inspection and packaging The director of manufacturing analyzed each of the operations and concluded that if the company produces a medium-priced standard model, each bag will require 7/10 hour in the cutting and dyeing department, 1/2 hour in the sewing department, 1 hour in the finishing department, and 1/10 hour in the inspection and packaging department. The more expensive deluxe model will require 1 hour for cutting and dyeing, 5/6 hour for sewing, 2/3 hour for finishing, and 1/4 hour for inspection and packaging. This production information is summarized in the following table: Production Time (hours) Department Standard Bag Deluxe Bag Cutting and Dyeing 7/10 1 Sewing 1/2 5/6 Finishing 1 2/3 Inspection and Packaging 1/10 1/4 Par Inc.'s production is constrained by a limited number of hours available in each department. After studying departmental workload projections, the director of manufacturing estimates that 630 hours for cutting and dyeing, 600 hours for sewing, 708 hours for finishing, and 135 hours for inspection and packaging will be available for the production of golf bags during the next three months. The accounting department analyzed the production data, assigned all relevant variable costs, and arrived at prices for both bags that will result in a profit contribution of $10 for every standard bag and $9 for every deluxe bag produced. Let us now develop a mathematical model of the Par, Inc., problem that can be used to determine the number of standard bags and the number of deluxe bags to produce in order to maximize total profit contribution. For each of the following independent situations, select the correct graph which shows the optimal solution and the total profit contribution: b. A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.) a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag. (i) AD (ii) AD 800- 800- (i) AD (ii) AD 800- 800- Optimalgolution (0, 720) Z= 12960 700- 700- 700- 700- 600- 600- 600- 600- 500- 500- 500- 500- 400- 400- Optimal solution (300, 420) Z= 10560 400- 400- 300- 300- Optimal solution (540, 252) Z- 13068 300- 300- 200- 200- 200- Optimal solution (708, 0) Z- 14160 100 200 30 400 500 600 700 200- 100- 100- 100- 100- 0- 100 200 300 400 500 600 700 100 20 300 400 50 600 700 100 200 300 400 500 600 700 (iii) B00 AD (iv) AD 800- (ii) AD AD 800- 700- 700- Optimalçolution (0, 720) Z= 12960 700- 700- 60- 600- 600- 600- 500- 500- 500- 500- 400- 400- Optimal solution (300, 420) Z= 10560 400- 400- 300 300- Optimal solution (540, 252) Z- 13068 300- 300- 200- 200- 200- 200- Optimal solution (708, 0) z- 14160 100 200 300 400 số0 600 100- 100- 100- 100- 100 200 300 400 500 60o 700 700 0- 100 200 300 400 500 600 700 100 200 300 400 500 600 700 c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A + 9B is the appropriate objective function.) (i) AD (ii) AD 800- 800- 700- 700- 600- 600- 500- 500- 400- 400- 300- 300- Optimal solution (540, 252) Z- 9068 Optimal solution (540, 252) Z-7768 200- 200- 100- 100- 100 200 300 400 s00 6do 70 100 200 30 400 500 600 70 (ii) AD (iv) AD 800- 800- 700- 700- 600- 600- 500- 500- Optimal solutio (300, 420) Z- 6780 400- 400- 300- 300- Optimal solution (540, 252) Z- 7768 200- 200- 100- 100- 100 200 300 400 500 600 100 200 300 400 500 600 700
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