Concept explainers
a)
To solve: The linear programming problem and answer the questions.
Introduction:
Linear programming:
Linear programming is a mathematical modelling method where a linear function is maximized or minimized taking into consideration the various constraints present in the problem. It is useful in making quantitative decisions in business planning.
a)
Explanation of Solution
Given information:
Calculation of coordinates for each constraint and objective function:
Constraint 1:
Constraint 2:
Constraint 3:
Constraint 4:
Objective function:
The problem is solved with iso-cost line method.
Graph:
(1) Optimal value of the decision variables and Z:
The coordinates for the cost line is (45, 55). The cost line is moved towards the origin. The lowest at which the cost line intersects in the feasible region will be the optimum solution. The following equation are solved as simultaneous equation to find optimum solution.
Solving (1) and (2) we get,
The values are substituted in the objective function to find the objective function value.
Optimal solution:
(2)
None of the constraints are having slack. All ≤ constraints are binding.
(3)
Protein and T constraint have surplus.
Protein:
The surplus is 92 (272 – 180).
T:
The surplus is 10 (20– 10).
(4)
The protein constraint is redundant because, it does not intersect at any point in the feasible region.
b)
To solve: The linear programming problem and answer the questions.
Introduction:
Linear programming:
Linear programming is a mathematical modelling method where a linear function is maximized or minimized taking into consideration the various constraints present in the problem. It is useful in making quantitative decisions in business planning.
b)
Explanation of Solution
Given information:
Calculation of coordinates for each constraint and objective function:
Constraint 1:
Constraint 2:
Constraint 3:
Objective function:
The problem is solved with iso-cost line method.
Graph:
(1) Optimal value of the decision variables and Z:
The coordinates for the cost line is (12, 8). The cost line is moved towards the origin. The lowest at which the cost line intersects in the feasible region will be the optimum solution. The following equation are solved as simultaneous equation to find optimum solution.
Solving (1) and (2) we get,
The values are substituted in the objective function to find the objective function value.
Optimal solution:
(2)
Constraint F is having slack as shown below.
The slack is 4.6 (12 – 7.4).
(3)
There are no surplus. D and E constraints with ≥ are binding.
(4)
There are no redundant constraints
Want to see more full solutions like this?
Chapter 19 Solutions
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
- Emotional intelligence is defined as the ability to understand and manage your emotions, as well as recognize and influence the emotions of those around you. True Falsearrow_forwardAt the Ford automobile Highland plant, assume the one-millionth vehicle was produced in 1916 at a cost of $8084 (in 2013 US$), by how much did the Ford company reduce his cost with each doubling of cumulative output from 1916 to 1927?arrow_forwardAt the Ford automobile Highland plant,in 1913, how long did the average worker stay with the plant and what was the average tenure of a worker?arrow_forward
- Community Federal Bank in Dothan, Alabama, recently increased its fees to customers who use employees as tellers. Management is interested in whether its new tee policy has increased the number of customers now using its automatic teller machines to that point that more machines are required. The following table provides the number of automatic teller transactions by week. Use trend projection with regression to forecast usage for weeks 13-16.arrow_forwardDavison Electronics manufactures three LED television monitors, identified as Model A, Model B, and Model C. Davison Electronics four manufacturing plants. Each model has its lowest possible production cost when produced at Plant 1. However, Plant 1 does not have the capacity to handle the total production of all three models. As a result, at least some of the production must be routed to the other manufacturing plants. The following table shows the minimum production requirements for next month, the plant capacities in units per month, and the production cost per unit at each plant: Model Production Cost per Unit Minimum Production Requirements Plant 1 Plant 2 Plant 3 Plant 4 A $25 $28 $37 $34 48,000 B $26 $35 $36 $41 75,000 C $20 $31 $26 $23 60,000 Production Capacity 65,000 50,000 32,000 43,000 Davison’s objective is to determine the cost-minimizing production planarrow_forwardAnecdotally, entrepreneurs frequently encounter two critical dilemmas in managing human resources: the timing of hiring and the decision regarding hiring a generalist versus a specialist for their growing venture. Deciding when to expand a team is crucial, as premature hiring (i.e., hiring too soon) can strain resources, while delayed hiring (i.e., hiring too late) might hinder growth opportunities. Moreover, the choice between hiring a generalist or a specialist depends on the specific needs and stage of the venture, with each option presenting distinct advantages and challenges. To address these issues, a management scholar seeks to identify the factors shaping the hiring cycle throughout the entrepreneurial journey and to understand the criteria for choosing between generalists and specialists at various stages of a venture. The scholar has assembled a sample of 20 experienced South African entrepreneurs who have encountered both failure and success in the financial technology…arrow_forward
- 3. [25 pts.] Four projects are available for investment. The projects require the cash flows and yield the net present values (NPV) (in millions) shown in the following table. Project id. 1 2 Cash outflow at time 0 (million Lira) 8 8 NPV (million Lira) 12 11 3 4 6 5 8 6 If 20 million Lira is available for investment at time 0, find the investment plan that maximizes NPV. All investments are required to be 0 or 1 (fractional investment values are not permitted). a. Formulate the mathematical model. (Write the decision variables, objective function and the constraints.) [10 pts.] b. Find the optimal solution by using Branch and Bound method (Draw the branch and bound tree clearly, write also lower bounds(LB)) (Left branches x=0, right branches x =1) [15 pts.].arrow_forwardexamine the production concept and operations management, what are the key steps required to achieve success? Be specific in your response.arrow_forwardProduce a 3000 report with references on one international organization of your choice and Address the following: Provide a brief introduction of the organisation and sector it operates in, including its mission and vision statements, its core values, a summary of its financial performance and a general overview of the business’s operational activities. From the relevant literature explain the Total Quality Management (TQM) processes the chosen organization follows and identify one quality challenge/issue that the organization faced or is currently facing. Explain how the organization managed/or still managing the particular quality challenge/issue. Critically analyze whether the organization failed or succeeded in achieving and maintaining quality performance. Provide a few critical recommendations for business managers in order to highlight the importance of Total Quality Management (TQM) within an organization.arrow_forward
- 問題2 Production system design involves determining the arrangement of workstations and the... O allocation of resources to workstations design of the process O production schedule all of the abovearrow_forwardElaborate on the need for and the benefits of an effective supply chain management (SCM) system in the context of a globalized and networked economy. In your answer, explain how organizations like Dell and Hewlett-Packard leverage supply chain networks to maintain competitiveness, and analyse the impact of globalization, technological advancements, and business environment changes on supply chain structures. Additionally, evaluate the key components of SCM, including distribution network configuration, inventory management, and cash-flow management, and discuss how these components contribute to creating an effective and integrated supply chain. (15) 3.2. Critically evaluate the requirements for effective inventory management within an organization. In your answer, discuss the importance of inventory accounting systems, the role of cost information (holding, ordering, and shortage costs), and the significance of classification systems like ABC analysis. Additionally, analyse how…arrow_forwardAssess the role of EDI in ensuring supply chain security and data integrity. How does EDI contribute to reducing vulnerabilities in supply chain operations, and what best practices should organizations adopt to maintain a secure and reliable EDI system? (10) 1.3. Examine how the adoption of modern EDI systems influences the strategic decision-making process in supply chain management. How does EDI provide supply chain managers with actionable insights, and what are the implications of these insights for long-term supply chain planning? (10) 1.4. Evaluate the potential challenges and risks associated with the modernization of EDI systems in supply chain management. How can organizations effectively manage these challenges to ensure successful EDI implementation and ongoing optimization? (10)arrow_forward
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,