मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

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

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प्रश्न

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

रिकाम्या जागा भरा

उत्तर

y ≤ x

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Linear Programming Problem (L.P.P.)
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.6: Linear Programming - Q.3 (C)

संबंधित प्रश्‍न

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 manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to the machine shop for finishing. The number of man-hours of labour required in each shop for production of A and B per unit and the number of man-hours available for the firm is as follows :

Gadgets Foundry Machine shop
A 10 5
B 6 4
Time available (hour) 60 35

Profit on the sale of A is ₹ 30 and B is ₹ 20 per units. Formulate the L.P.P. to have maximum profit.


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.


The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs ₹ 20 per kg and sand costs of ₹ 6 per kg. Strength consideration dictates that a concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand. Form the L.P.P. for the cost to be minimum.


Solve the following LPP by graphical method:

Maximize z = 11x + 8y, subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0


Select the appropriate alternatives for each of the following question:

The value of objective function is maximum under linear constraints


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Maximize z = 6x + 10y subject to 3x + 5y ≤ 10, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.


Solve the following LPP:

Maximize z = 2x + 3y subject to x - y ≥ 3, x ≥ 0, y ≥ 0.


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

- 11x - 55 ≤ 0


Solve the following LPP:

Minimize z = 4x + 2y

Subject to 3x + y ≥ 27, x + y ≥ 21, x + 2y ≥ 30, x ≥ 0, y ≥ 0


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Machine  Mixer Food Processor Available time
A 3 3 36
B 5 2 50
C 2 6 60

How many mixers and food processors should be produced in order to maximize the profit?


A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 on 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, 60 hours per week respectively. Formulate the Linear programming problem to maximize the profit.


Choose the correct alternative :

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A train carries at least twice as many first class passengers (y) as second class passengers (x) The constraint is given by_______


State whether the following is True or False :

The point (1, 2) is not a vertex of the feasible region bounded by 2x + 3y ≤ 6, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.


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Solve the following linear programming problems by graphical method.

Maximize Z = 22x1 + 18x2 subject to constraints 960x1 + 640x2 ≤ 15360; x1 + x2 ≤ 20 and x1, x2 ≥ 0.


A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1 and two minutes on M2, While B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hrs 30 minutes while M2 is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.


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