NMIMS BBA – B.Com Operations Research Solved Answer Assignment
Operations Research
1) A company manufactures two products (A and Band the profit per unit sold is Rs 3 and Rs 5 respectively. Each product must be assembled on a particular machine, each unit of product a takes 12 minutes of assembly time and each unit of product B takes 25 minutes of assembly time. The company estimates that the machine used for assembly has an effective working week of only 30 hours (due to maintenance/breakdown). Technological constraints mean that for every 5 units of product A produced at least 2 units of product B must be produced. Formulate the problem of how much of each product to produce as a linear program and find the points of intersection for maximization. The company has been offered the chance to hire an extra machine, thereby doubling the effective assembly time available. What is the maximum amount you would be prepared to pay (per week) for the hire of this machine and why?(10 marks)
ANS:
Introduction
The news of the chance to employ an additional machine sent excitement into the business. This was a game-changer, a possibility to increase their assembly time and ramp up their production to new heights. The case of satisfying their customers’ needs quicker and more effectively than in the past was now within their grasp. The thought of having extra equipment relieved the team, working tirelessly to fulfill due dates.
Concepts and Applications
Allow x to be the number of units of product A to create and y to be the variety of units of product B per week.
The goal is to maximize earnings, which are offered by:
To conclude, the company has to consider the competitive landscape and the possible influence of not employing the extra device. The price of not using the different machine may be greater than hiring it if rivals are raising their manufacturing capacity and getting market share.
2) A firm produces three products A, B, and C each of which passes through three different departments fabrication, finishing, and packaging. Each unit of product A requires 3, 4 and 2 hours, B requires 5, 4 and 4 hours and C requires 2, 4 and 5 hours in 3 departments respectively. The maximum capacity available is 60 hours in fabrication department, 72 hours in finishing and 100 hours in packaging department. If unit contribution is Rs. 5 for A, Rs. 10 for B and Rs. 3 for C. Then determine number of units of each product so that total contribution to cost is maximized and also determine if any capacity would remain unutilized using simple method. (10 marks)
ANS:
Introduction
A simple method is a powerful tool for optimization. It is a repetitive process that seeks to take full advantage of or reduce an objective feature based on linear restrictions. The algorithm is based upon the idea of a viable region, which is the set of all points that please the offered constraints. The optimal option is the point within the possible area that maximizes or decreases the objective function.
Concepts and Applications
To resolve this trouble by using the simplex technique, we first need to define decision variables and constraints.
Choice variables:
Let x, y, and z be the number of items A, B, and C units.
Purpose feature:
The total contribution to expense is offered by:
Z = 5x + 10y + 3z
Constraints:
The constraints are based on the maximum capacity available in each department. They are as follows:
Fabrication department:
3x + 5y + 2z ≤ 60
Finishing department:
4x + 4y + 4z ≤ 72
Packaging department:
2x + 4y + 5z ≤ 100
Non-negativity constraints:
X, y, z ≥ 0
Conclusion
The simplex approach is a popular direct programming algorithm widely used to optimize options for complex optimization problems. It is a widely-used optimization technique involving utilizing linear algebra to solve formulas to determine the optimum worths for choice variables.
3) a) An investor is considering investing in two securities ‘A’ and ‘B’. The risk and return associated with these securities are different. Security ‘A’ gives a return of 9% and has a risk factor of 5 on a scale of zero to 10. Security ‘B’ gives a return of 15% but has a risk factor of 8 on a scale of zero to 10. The total amount to be invested is Rs. 500000/- Total minimum returns on the investment should be 12%. The maximum combined risk should not be more than 6. Formulate as Linear Programming Problem (LPP). (5 marks)
ANS:
Introduction
Among the main benefits of an LLP for safety investment is the limited obligation defense it provides to its companions. This implies that each partner’s personal properties are secured from the partnership’s liabilities, consisting of any economic or legal obligations that might arise.
Concepts and Applications
To develop this issue as a direct shows trouble (LPP), we need to define our decision variables, unbiased features, and restraints.
Decision Variables:
Be the quantity x let purchased Safety and security A, and y be the amount purchased Safety and security B.
Objective Function:
We want to maximize the total return on our investment, which can be stood for as:
Maximize 0.09x + 0.15y
Conclusion
The decision variables x and y represent the amount spent on Protection A and Safety. Security B. LLPs are becoming famous for safety and security financial investment firms due to their benefits.
3) b) There is a small company in the town of Mysore which has recently become engaged in the production of office furniture. The company manufactures tables, desks, and chairs. The production of a table requires 8 kgs of wood and 5 kgs of metal and is sold for Rs 8000; a desk uses 6 kgs of wood and 4 kgs of metal and is sold for Rs 6000; and a chair requires 4 kgs of both metal and wood and is sold for Rs 5000. We would like to determine the revenue-maximizing strategy for this company, given that their resources are limited to 100 kgs of wood and 60 kgs of metal. How will a much bigger company (like IKEA) determine the appropriate amount of money that should be offered for a unit of each type of resource, such that the offer will be acceptable to the smaller company while minimizing the expenditures of the larger company?
ANS:
Introduction
When a giant firm like IKEA needs to identify the appropriate quantity of money to offer for a system of each source type, it usually takes a calculated strategy. The firm will certainly assess the worth and deficiency of the resource, along with the competitive landscape and the negotiating power of the smaller business.
Concepts and Applications
To identify the revenue-maximizing strategy for the small company, we need to identify the number of systems each item must be created to optimize income while staying within the constraints of minimal sources. Let’s define the decision variables as complying with the following:
X1 = variety of tables generated
X2 = variety of desks created
X3 = variety of chairs produced
After that, the objective function (profits) can be revealed as follows:
R = 8000×1 + 6000×2 + 5000×3
Conclusion
To identify a suitable deal, IKEA might think about variables such as the current market price for the resources, the availability of different distributors, and the bargaining power of the small company.
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