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

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

Question

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

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

Accepted Answer

Answer :