Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Customer D1 1 D2 2 D3 3 D4 4 Clifton Springs 1 $32 $34 $32 $40 Danville 2 $34 $30 $28 $38 The plant capacities and customer orders are as follows. Plant Capacity (units) Clifton Springs 5,000 Danville 3,000 Distributor Orders (units) D1 2,000 D2 5,000 D3 3,000 D4 2,000 (a) Develop a network model and a linear programming formulation of this problem. (i) network model (Submit a file with a maximum size of 1 MB.) This answer has not been graded yet. (ii) linear programming formulation Let xij = number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max s.t.Orders from Clifton Springs Orders from Danville Orders from/for Dummy Node Orders for D1 Orders for D2 Orders for D3 Orders for D4 xij ≥ 0 for all i, j. (b) How many units should each plant produce for each customer to maximize profits? Optimal Solution Units Cost Clifton Springs–D1 $ Clifton Springs–D2 $ Clifton Springs–D3 $ Clifton Springs–D4 $ Danville–D1 $ Danville–D2 $ Danville–D3 $ Danville–D4 $ Total Cost $ (c) Which customer demands will not be met? Distributor 1 will have a shortfall of units. Distributor 2 will have a shortfall of units. Distributor 3 will have a shortfall of units. Distributor 4 will have a shortfall of units.
Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Customer D1 1 D2 2 D3 3 D4 4 Clifton Springs 1 $32 $34 $32 $40 Danville 2 $34 $30 $28 $38 The plant capacities and customer orders are as follows. Plant Capacity (units) Clifton Springs 5,000 Danville 3,000 Distributor Orders (units) D1 2,000 D2 5,000 D3 3,000 D4 2,000 (a) Develop a network model and a linear programming formulation of this problem. (i) network model (Submit a file with a maximum size of 1 MB.) This answer has not been graded yet. (ii) linear programming formulation Let xij = number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max s.t.Orders from Clifton Springs Orders from Danville Orders from/for Dummy Node Orders for D1 Orders for D2 Orders for D3 Orders for D4 xij ≥ 0 for all i, j. (b) How many units should each plant produce for each customer to maximize profits? Optimal Solution Units Cost Clifton Springs–D1 $ Clifton Springs–D2 $ Clifton Springs–D3 $ Clifton Springs–D4 $ Danville–D1 $ Danville–D2 $ Danville–D3 $ Danville–D4 $ Total Cost $ (c) Which customer demands will not be met? Distributor 1 will have a shortfall of units. Distributor 2 will have a shortfall of units. Distributor 3 will have a shortfall of units. Distributor 4 will have a shortfall of units.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Concept explainers
Critical Path Method
The critical path is the longest succession of tasks that has to be successfully completed to conclude a project entirely. The tasks involved in the sequence are called critical activities, as any task getting delayed will result in the whole project getting delayed. To determine the time duration of a project, the critical path has to be identified. The critical path method or CPM is used by project managers to evaluate the least amount of time required to finish each task with the least amount of delay.
Cost Analysis
The entire idea of cost of production or definition of production cost is applied corresponding or we can say that it is related to investment or money cost. Money cost or investment refers to any money expenditure which the firm or supplier or producer undertakes in purchasing or hiring factor of production or factor services.
Inventory Management
Inventory management is the process or system of handling all the goods that an organization owns. In simpler terms, inventory management deals with how a company orders, stores, and uses its goods.
Project Management
Project Management is all about management and optimum utilization of the resources in the best possible manner to develop the software as per the requirement of the client. Here the Project refers to the development of software to meet the end objective of the client by providing the required product or service within a specified Period of time and ensuring high quality. This can be done by managing all the available resources. In short, it can be defined as an application of knowledge, skills, tools, and techniques to meet the objective of the Project. It is the duty of a Project Manager to achieve the objective of the Project as per the specifications given by the client.
Topic Video
Question
100%
Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative.
| Plant | Customer | |||
|---|---|---|---|---|
| D1 1 | D2 2 | D3 3 | D4 4 | |
| Clifton Springs 1 | $32 | $34 | $32 | $40 |
| Danville 2 | $34 | $30 | $28 | $38 |
The plant capacities and customer orders are as follows.
| Plant | Capacity (units) |
|---|---|
| Clifton Springs | 5,000 |
| Danville | 3,000 |
| Distributor Orders (units) | |
|---|---|
|
D1
|
2,000 |
|
D2
|
5,000 |
|
D3
|
3,000 |
|
D4
|
2,000 |
(a)
Develop a network model and a linear programming formulation of this problem.
(i)
network model (Submit a file with a maximum size of 1 MB.)
This answer has not been graded yet.
(ii)
linear programming formulation
Let xij = number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.)
Max
s.t.Orders from Clifton Springs
Orders from Danville
Orders from/for Dummy Node
Orders for D1
Orders for D2
Orders for D3
Orders for D4
xij ≥ 0 for all i, j.
(b)
How many units should each plant produce for each customer to maximize profits?
Optimal Solution
| Units | Cost | |
|---|---|---|
|
Clifton Springs–D1
|
$ | |
|
Clifton Springs–D2
|
$ | |
|
Clifton Springs–D3
|
$ | |
|
Clifton Springs–D4
|
$ | |
|
Danville–D1
|
$ | |
|
Danville–D2
|
$ | |
|
Danville–D3
|
$ | |
|
Danville–D4
|
$ | |
| Total Cost | $ |
(c)
Which customer demands will not be met?
Distributor 1 will have a shortfall of units.
Distributor 2 will have a shortfall of units.
Distributor 3 will have a shortfall of units.
Distributor 4 will have a shortfall of units.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.