मराठी

The feasible region corresponding to the linear constraints of a Linear Programming Problem is given below. Which of the following is not a constraint to the given Linear Programming Problem?

Advertisements
Advertisements

प्रश्न

The feasible region corresponding to the linear constraints of a Linear Programming Problem is given below.


Which of the following is not a constraint to the given Linear Programming Problem?

पर्याय

  • x + y ≥ 2

  • x + 2y ≤ 10

  • x – y ≥ 1

  • x – y ≤ 1

MCQ
Advertisements

उत्तर

x – y ≥ 1

Explanation:

We observe, (0, 0) does not satisfy the inequality x – y ≥ 1

So, the half plane represented by the above inequality will not contain origin

Therefore, it will not contain the shaded feasible region.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2023-2024 (March) Board Sample Paper

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Make it as a LPP and solve it graphically.


A retired person wants to invest an amount of Rs. 50, 000. His broker recommends investing in two type of bonds ‘A’ and ‘B’ yielding 10% and 9% return respectively on the invested amount. He decides to invest at least Rs. 20,000 in bond ‘A’ and at least Rs. 10,000 in bond ‘B’. He also wants to invest at least as much in bond ‘A’ as in bond ‘B’. Solve this linear programming problem graphically to maximise his returns.


Minimum and maximum z = 5x + 2y subject to the following constraints:

x-2y ≤ 2

3x+2y ≤ 12

-3x+2y ≤ 3

x ≥ 0,y ≥ 0


Solve the following L.P.P. graphically Maximise Z = 4x + y 

Subject to following constraints  x + y ≤ 50

3x + y ≤ 90,

x ≥ 10

x, y ≥ 0


Solve the following L.P.P graphically: Maximise Z = 20x + 10y

Subject to the following constraints x + 2y ≤ 28,

3x + y ≤ 24,

x ≥ 2,

 x, y ≥ 0


Minimize Z = 30x + 20y
Subject to 

\[x + y \leq 8\]
\[ x + 4y \geq 12\]
\[5x + 8y = 20\]
\[ x, y \geq 0\]


Maximize Z = x + y
Subject to

\[- 2x + y \leq 1\]
\[ x \leq 2\]
\[ x + y \leq 3\]
\[ x, y \geq 0\]


Find the minimum value of 3x + 5y subject to the constraints
− 2x + y ≤ 4, x + y ≥ 3, x − 2y ≤ 2, x, y ≥ 0.


A factory manufactures two types of screws, A and B, each type requiring the use of two machines - an automatic and a hand-operated. It takes 4 minute on the automatic and 6 minutes on the hand-operated machines to manufacture a package of screws 'A', while it takes 6 minutes on the automatic and 3 minutes on the hand-operated machine to manufacture a package of screws 'B'. Each machine is available for at most 4 hours on any day. The manufacturer can sell a package of screws 'A' at a profit of 70 P and screws 'B' at a profit of Rs 1. Assuming that he can sell all the screws he can manufacture, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.


A manufacturer makes two types A and B of tea-cups. Three machines are needed for the manufacture and the time in minutes required for each cup on the machines is given below:

  Machines
I II III
A
B
12
6
18
0
6
9

Each machine is available for a maximum of 6 hours per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise, show that 15 tea-cups of type A and 30 of type B should be manufactured in a day to get the maximum profit.


A gardener has supply of fertilizer of type I which consists of 10% nitrogen and 6% phosphoric acid and type II fertilizer which consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, he finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop. If the type I fertilizer costs 60 paise per kg and type II fertilizer costs 40 paise per kg, determine how many kilograms of each fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?


A producer has 30 and 17 units of labour and capital respectively which he can use to produce two type of goods x and y. To produce one unit of x, 2 units of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of y. If x and y are priced at Rs 100 and Rs 120 per unit respectively, how should be producer use his resources to maximize the total revenue? Solve the problem graphically.


A company sells two different products, A and B. The two products are produced in a common production process, which has a total capacity of 500 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of unit of A that can be sold is 70 and that for B is 125. If the profit is Rs 20 per unit for the product A and Rs 15 per unit for the product B, how many units of each product should be sold to maximize profit?


A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at ₹100 and ₹120 per unit respectively, how should he use his resources to maximise the total revenue? Form the above as an LPP and solve graphically. Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?


A company manufactures two types of cardigans: type A and type B. It costs ₹ 360 to make a type A cardigan and ₹ 120 to make a type B cardigan. The company can make at most 300 cardigans and spend at most ₹ 72000 a day. The number of cardigans of type B cannot exceed the number of cardigans of type A by more than 200. The company makes a profit of ₹ 100 for each cardigan of type A and ₹ 50 for every cardigan of type B. 

Formulate this problem as a linear programming problem to maximize the profit to the company. Solve it graphically and find the maximum profit.


Find the feasible solution of linear inequation 2x + 3y ≤ 12, 2x + y ≤ 8, x ≥ 0, y ≥ 0 by graphically


The minimum value of z = 10x + 25y subject to 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≥ 5 is ______.


The maximum value of z = 6x + 8y subject to x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0 is ______.


For the LPP, maximize z = x + 4y subject to the constraints x + 2y ≤ 2, x + 2y ≥ 8, x, y ≥ 0 ______.


A set of values of decision variables which satisfies the linear constraints and nn-negativity conditions of an L.P.P. is called its ____________.


The feasible region (shaded) for a L.P.P is shown in the figure. The maximum Z = 5x + 7y is ____________.


Solve the following Linear Programming Problem graphically:

Maximize: z = – x + 2y,

Subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.


Solve the following Linear Programming Problem graphically.

Maximise Z = 5x + 2y subject to:

x – 2y ≤ 2,

3x + 2y ≤ 12,

– 3x + 2y ≤ 3,

x ≥ 0, y ≥ 0


If x – y ≥ 8, x ≥ 3, y ≥ 3, x ≥ 0, y ≥ 0 then find the coordinates of the corner points of the feasible region.


Which statement defines a feasible solution?


Which point is an infeasible solution?


For a bounded feasible region, where do the maximum and minimum values occur?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×