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1) A company manufactures two products (A and B) and 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?

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 simplex method.

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).

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?

Old Assignment

Q1. A manufacturer produces three types of plastic fixtures. The time required for molding, trimming, and packaging is given in the table below: (Times are given in hours per dozen fixtures.)

How many dozens of each type of fixture should be produced to obtain a maximum profit?

Q2. The advertising alternatives for a company include television, radio, and newspaper advertisements. The costs and estimates for audience coverage are given in table below:

The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?

Q3.a. A manufacturer of certain household goods caters primarily to the south Indian market. At present, the manufacturer has located six stock points in the major south Indian cities of Hyderabad, Mysore, Chennai, Kochi, Pune, and Vizag to cater to the demand. There are four warehouses from which the components are distributed. In order to save on the cost of operations, the warehouses are typically located away from these cities in different locations. Identify the least cost schedule for deciding which warehouse will send the items to the cities.

3.b. Suppose the company has received a proposal for setting up another warehouse (Warehouse E) with a capacity of 900 units. The location of the warehouse is such that the unit costs of transporting to the six cities are as follows: Hyderabad–45, Mysore– 75, Chennai–30, Kochi–65, Pune–90 and Vizag–80. The company would like to know how the allocation will change if the warehouse is made operational and the likely cost impact on the operation of the system.

Operations Research NMIMS Solution

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