# Questions And Answers On Linear Programming Pdf

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Wheat is Rs. He has capacity to store quintal cereal. He earns the profit Rs.

## Linear Programming Class 12 Mathematics Important Questions

These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years.

There are around set of solved Chapter 12 Linear Programming Mathematics Extra Questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Board Exam. Download as PDF. In order to supplement daily diet, a person wishes to take some X and some wishes Y tablets.

The contents of iron, calcium and vitamins in X and Y in milligram per tablet are given as below:. The person needs at least 18 milligram of iron, 21 milligram of calcium and 16 milligram of vitamins. The price of each tablet of X and Y is Rs 2 and Re 1 respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?

A factory owner purchases two types of machine A and B for his factory. The requirements and the limitations for the machines are as follows,. He has maximum area m 2 available and 72 skilled labours who can operate both the machines. How many machines of each type should he buy to maximize the daily out put?

A factory makes tennis rackets and cricket bats. A tennis racket takes 1. Chapter 12 Linear Programming. The minimum value occurs at 0,8 Intersection Linear constraints maximum Let number of necklaces and bracelets produced by firm per day be x and y, respectively. Given that the maximum number of both necklaces and bracelets that firm can handle per day is almost Let z be the objective function which represents the total maximum profit.

Thus, we see that 8 is the minimum value of Z at the corner point 1, 6. Here we see that the feasible region is unbounded. Therefore, 8 may or may not be the minimum value of Z. If it has common point, then 8 will not be the minimum value of Z, otherwise 8 will be the minimum value of Z. Thus, from the graph it is clear that, it has no common point.

Hence, the person should take 1 unit of X tablet and 6 unit of Y tablets to satisfy the given requirements and at the minimum cost of Rs 8. Let x machines of type A and y machines of type B be bought and let Z be the daily output. Hence, either 6 machine of type A and no machine of type B or 2 machine of type A and 6 machine of type B be used to have maximum output.

The feasible region R is unbounded. Therefore, a minimum of Z may or may not exist. If it exists, it will be at the corner point Fig. So, the smallest value 13 is the minimum value of Z. The feasible region OBEC is bounded, so, minimum value will obtain at a comer point of this feasible region.

Let the manufacturer produce x units of type A circuit and y units of type B circuits. From the given information, we have following corresponding constraint table. Now, we have the following mathematical model for the given problem.

Now, we see that 3 is the smallest value of Z at the corner point 0, 3. Note that here we see that the region is unbounded, therefore 3 may or may not be the minimum value of Z. From the shown graph above, it is clear that there is no point in common with feasible region and hence Z has minimum value of 3 at 0, 3.

Hence, kg of fertilizer F 1 and 80 kg of fertilizer F 2 should be used so that nutrient requirements are met at minimum cost of Rs Let the number of Tenis rackets and the number of cricket bats to be made in a day be x and y respectively.

Let Z represent the objective function which represent the sum of the wages. So, it passes through the points with coordinates 0, 6 and 10, 0. So, it passes through the points with coordinates 0, 8 and 8, 0. On solving Eqs.

The corner points are A 0, 8 , P 5, 3 and B 10, 0. The values of Z at corner points are as follows:. As the feasible region is unbounded, therefore may or may not be the minimum value of Z. Hence, The minimum labour cost is Rs. Save my name, email, and website in this browser for the next time I comment. Download Now. A linear programming problem is one that is concerned with. A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs per bag, contains 3 units of nutritional element A, 2.

Brand Q costing Rs per bag contains 1. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?

The feasible solution for an LPP is shown in Figure. Minimum of Z occurs at. A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is If the profit on a necklace is Rs and that on a bracelet is Rs Formulate on L. It is being given that at least one of each must be produced.

The contents of iron, calcium and vitamins in X and Y in milligram per tablet are given as below: Tablets Iron Calcium Vitamin X 6 3 2 Y 2 3 4 The person needs at least 18 milligram of iron, 21 milligram of calcium and 16 milligram of vitamins.

The requirements and the limitations for the machines are as follows, Machine Area Occupied Labour force Daily on each machine output in units A m 2 12 men 60 B m 2 8 men 40 He has maximum area m 2 available and 72 skilled labours who can operate both the machines.

A manufacturer of electronic circuits has a stock of resistors, transistors and capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors.

Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs 50 and that on type B circuit is Rs 60, formulate this problem as a LPP so that the manufacturer can maximise his profit. The feasible region for a LPP is shown in Fig. Find the minimum value of Z, if it exists. There are two types of fertilizers F 1 and F 2. After testing the soil conditions, a farmer finds that she needs atleast 14kg of nitrogen and 14 kg of phosphoric acid for her crop.

What is the minimum cost? What number of rackets and bats must be made if the factory is t work at full capacity? If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity. Two tailors A and B earn Rs.

A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. How many days shall each work, if it is desired to produce at least 60 shirts and 32 pants at a minimum labour cost? Make it as an LPP and solve the problem graphically.

## Practice Problems

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research OR. They are now available for use by any students and teachers interested in OR subject to the following conditions. A full list of the topics available in OR-Notes can be found here. A company makes two products X and Y using two machines A and B. Each unit of X that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B.

of linear inequalities in two variables and their solutions by graphical problem. Linear programming problems are of much interest because of their wide profit? To answer this question, let us try to formulate the problem mathematically.

## Linear programming

Multiple Choice Questions have been coming in Class 12 Linear Programming exams, thus do MCQs to test understanding of important topics in the chapters. Download latest questions with multiple choice answers for Class 12 Linear Programming in pdf free or read online in online reader free. Download in pdf free by clicking on links below -. You should also carefully go through the syllabus for Class 12 Linear Programming and download MCQs for each topics which you have studied.

These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. There are around set of solved Chapter 12 Linear Programming Mathematics Extra Questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Board Exam. Download as PDF.

Linear programming LP , also called linear optimization is a method to achieve the best outcome such as maximum profit or lowest cost in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming also known as mathematical optimization. More formally, linear programming is a technique for the optimization of a linear objective function , subject to linear equality and linear inequality constraints.

#### Solving Linear Programming Problems Graphically

Спасибо, - улыбнулся Беккер и повернулся, собираясь уходить. Консьерж бросил внимательный взгляд в его спину, взял конверт со стойки и повернулся к полке с номерными ячейками. Когда он клал конверт в одну из ячеек, Беккер повернулся, чтобы задать последний вопрос: - Как мне вызвать такси. Консьерж повернул голову и. Но Беккер не слушал, что тот. Он рассчитал все .

Глаза немца сузились. - Ein Ring, - сказал Беккер. - Du hast einen Ring. У вас есть кольцо. - Проваливайте! - зарычал немец и начал закрывать дверь. Беккер не раздумывая просунул ногу в щель и открыл дверь. Но сразу же об этом пожалел.

Три месяца назад до Фонтейна дошли слухи о том, что от Стратмора уходит жена. Он узнал также и о том, что его заместитель просиживает на службе до глубокой ночи и может не выдержать такого напряжения. Несмотря на разногласия со Стратмором по многим вопросам, Фонтейн всегда очень высоко его ценил. Стратмор был блестящим специалистом, возможно, лучшим в агентстве.

Консьерж бросил внимательный взгляд в его спину, взял конверт со стойки и повернулся к полке с номерными ячейками. Когда он клал конверт в одну из ячеек, Беккер повернулся, чтобы задать последний вопрос: - Как мне вызвать такси. Консьерж повернул голову и .

- Я любил тебя. У нее свело желудок. - Останься со. В ее сознании замелькали страшные образы: светло-зеленые глаза Дэвида, закрывающиеся в последний раз; тело Грега Хейла, его сочащаяся кровь на ковре; обгорелый труп Фила Чатрукьяна на лопастях генератора.

* - Моя фамилия Халохот. - Его голос доносился как будто из его чрева.*

### 3 Comments

Xam Idea Class 12 Mathematics Solutions is a complete exam preparation textbook for senior secondary classes.

In business and in day-to-day living we know that we cannot simply choose to do something because it would make sense that it would unreasonably accomplish our goal.