मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

The point of which the maximum value of x + y subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x, ≥ 0, y ≥ 0 is is obtained at ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The point of which the maximum value of x + y subject to the constraints x + 2y ≤  70, 2x + y ≤ 95, x, ≥ 0, y ≥ 0 is is obtained at ______.

पर्याय

  • (30, 25)

  • (20, 35)

  • (35, 20)

  • (40, 15)

MCQ
रिकाम्या जागा भरा

उत्तर

The point of which the maximum value of x + y subject to the constraints x + 2y ≤  70, 2x + y ≤ 95, x, ≥ 0, y ≥ 0 is is obtained at (40, 15).

shaalaa.com
Linear Programming Problem (L.P.P.)
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Linear Programming - Miscellaneous exercise 7 [पृष्ठ २४२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 7 Linear Programming
Miscellaneous exercise 7 | Q 6 | पृष्ठ २४२

संबंधित प्रश्‍न

Which of the following statements is correct?


Find the feasible solution of the following inequation:

x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9,  x ≥ 0, y ≥ 0.


A company produces two types of articles A and B which requires silver and gold. Each unit of A requires 3 gm of silver and 1 gm of gold, while each unit of B requires 2 gm of silver and 2 gm of gold. The company has 6 gm of silver and 4 gm of gold. Construct the inequations and find feasible solution graphically.


A furniture dealer deals in tables and chairs. He has ₹ 1,50,000 to invest and a space to store at most 60 pieces. A table costs him ₹ 1500 and a chair ₹ 750. Construct the inequations and find the feasible solution.


A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 in magazines A and B per copy. These are processed on three Machines I, II, III. Magazine A requires 2 hours on Machine I, 5 hours on Machine II, and 2 hours on machine III. Magazine B requires 3 hours on machine I, 2 hours on machine II and 6 hours on Machine III. Machines I, II, III are available for 36, 50, and 60 hours per week respectively. Formulate the LPP to determine weekly production of magazines A and B, so that the total profit is maximum.


A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M1 and M2. A package of bulbs requires 1 hour of work on Machine M1 and 3 hours of work on Machine M2. A package of tubes requires 2 hours on Machine M1 and 4 hours on Machine M2. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. Formulate the LPP to maximize the profit, if he operates the machine M1, for almost 10 hours a day and machine M2 for almost 12 hours a day.


Minimize z = 6x + 2y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y  ≥ 3, x ≥ 0, y ≥ 0.


The maximum value of z = 5x + 3y subject to the constraints 3x + 5y ≤ 15, 5x + 2y ≤ 10, x, y ≥ 0 is ______.


The corner points of the feasible solution are (0, 0), (2, 0), `(12/7, 3/7)`, (0, 1). Then z = 7x + y is maximum at ______.


The half-plane represented by 4x + 3y >14 contains the point ______.


Solve the following LPP:

Maximize z = 5x1 + 6x2 subject to 2x1 + 3x2 ≤ 18, 2x1 + x2 ≤ 12, x1 ≥ 0, x2 ≥ 0.


Solve each of the following inequations graphically using XY-plane:

- 11x - 55 ≤ 0


Solve each of the following inequations graphically using XY-plane:

y ≤ - 3.5


Solve the following LPP:

Maximize z = 4x1 + 3x2 subject to
3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0. 


A chemical company produces a chemical containing three basic elements A, B, C, so that it has at least 16 litres of A, 24 litres of B and 18 litres of C. This chemical is made by mixing two compounds I and II. Each unit of compound I has 4 litres of A, 12 litres of B and 2 litres of C. Each unit of compound II has 2 litres of A, 2 litres of B and 6 litres of C. The cost per unit of compound I is ₹ 800 and that of compound II is ₹ 640. Formulate the problems as LPP and solve it to minimize the cost.


A company manufactures two types of chemicals A and B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B.

Raw Material \Chemical A B Availability
p 3 2 120
Q 2 5 160

The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. Formulate the problem as L.P.P. to maximize the profit.


Choose the correct alternative :

The corner points of the feasible region are (0, 0), (2, 0), `(12/7, 3/7)` and (0,1) then the point of maximum z = 7x + y


Choose the correct alternative :

The half plane represented by 3x + 2y ≤ 0 constraints the point.


Fill in the blank :

“A gorage employs eight men to work in its shownroom and repair shop. The constraints that there must be at least 3 men in showroom and at least 2 men in repair shop are ______ and _______ respectively.


State whether the following is True or False :

The feasible solution of LPP belongs to only quadrant I.


Which value of x is in the solution set of inequality − 2X + Y ≥ 17


Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0


Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points


State whether the following statement is True or False:

LPP is related to efficient use of limited resources


The variables involved in LPP are called ______


The constraint that in a particular XII class, number of boys (y) are less than number of girls (x) is given by ______


A company produces two types of products say type A and B. Profits on the two types of product are ₹ 30/- and ₹ 40/- per kg respectively. The data on resources required and availability of resources are given below.

  Requirements Capacity available per month
Product A Product B
Raw material (kgs) 60 120 12000
Machining hours/piece 8 5 600
Assembling (man hours) 3 4 500

Formulate this problem as a linear programming problem to maximize the profit.


Solve the following linear programming problems by graphical method.

Maximize Z = 20x1 + 30x2 subject to constraints 3x1 + 3x2 ≤ 36; 5x1 + 2x2 ≤ 50; 2x1 + 6x2 ≤ 60 and x1, x2 ≥ 0.


In the given graph the coordinates of M1 are


Given an L.P.P maximize Z = 2x1 + 3x2 subject to the constrains x1 + x2 ≤ 1, 5x1 + 5x2 ≥ 0 and x1 ≥ 0, x2 ≥ 0 using graphical method, we observe


Solve the following linear programming problem graphically.

Minimize Z = 200x1 + 500x2 subject to the constraints: x1 + 2x2 ≥ 10; 3x1 + 4x2 ≤ 24 and x1 ≥ 0, x2 ≥ 0.


Solve the following linear programming problem graphically.

Maximize Z = 3x1 + 5x2 subject to the constraints: x1 + x2 ≤ 6, x1 ≤ 4; x2 ≤ 5, and x1, x2 ≥ 0.


Solve the following linear programming problem graphically.

Maximize Z = 60x1 + 15x2 subject to the constraints: x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 and x1, x2 ≥ 0.


The point which provides the solution of the linear programming problem, Max.(45x + 55y) subject to constraints x, y ≥ 0, 6x + 4y ≤ 120, 3x + 10y ≤ 180, is ______ 


Solve the following LP.P.

Maximize z = 13x + 9y,

Subject to 3x + 2y ≤ 12,

x + y ≥ 4,

x ≥ 0,

y ≥ 0.


The optimal value of the objective function is attained at the ______ of feasible region.


The maximum value of Z = 9x + 13y subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0 is ______.


Solve the following LPP:

Maximize z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.


Two kinds of foods A and B are being considered to form a weekly diet. The minimum weekly requirements of fats, Carbohydrates and proteins are 12, 16 and 15 units respectively. One kg of food A has 2, 8 and 5 units respectively of these ingredients and one kg of food B has 6, 2 and 3 units respectively. The price of food A is Rs. 4 per kg and that of food B is Rs. 3 per kg. Formulate the L.P.P. and find the minimum cost.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×