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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

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प्रश्न

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

पर्याय

  • − 8

  • − 6

  • − 4

  • 12

MCQ

उत्तर

− 8

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Linear Programming Problem (L.P.P.)
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.7: Linear Programming Problems - MCQ

संबंधित प्रश्‍न

Which of the following statements is correct?


Find the feasible solution of the following inequations:

x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0


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.


In a cattle breading firm, it is prescribed that the food ration for one animal must contain 14. 22 and 1 units of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit of these two contains the following amounts of these three nutrients: 

Fodder → Fodder 1 Fodder 2
Nutrient ↓
Nutrients A 2 1
Nutrients B 2 3
Nutrients C 1 1

The cost of fodder 1 is ₹ 3 per unit and that of fodder 2 ₹ 2. Formulate the LPP to minimize the cost.


A company manufactures two types of fertilizers F1 and F2. Each type of fertilizer requires two raw materials A and B. The number of units of A and B required to manufacture one unit of fertilizer F1 and F2 and availability of the raw materials A and B per day are given in the table below:

Fertilizers→ F1 F2 Availability
Raw Material ↓
A 2 3 40
B 1 4 70

By selling one unit of F1 and one unit of F2, the company gets a profit of ₹ 500 and ₹ 750 respectively. Formulate the problem as LPP to maximize the profit.


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


Solve the following LPP by graphical method:

Maximize z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.


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


If the corner points of the feasible solution are (0, 0), (3, 0), (2, 1), `(0, 7/3)` the maximum value of z = 4x + 5y is ______.


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

4x - 18 ≥ 0


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

5y - 12 ≥ 0


A carpenter makes chairs and tables. Profits are ₹ 140 per chair and ₹ 210 per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by the following table:

Product → Chair (x) Table (y) Available time (hours)
Machine ↓
Assembling 3 3 36
Finishing 5 2 50
Polishing 2 6 60

Formulate the above problem as LPP. Solve it graphically


Choose the correct alternative :

Of all the points of the feasible region the optimal value of z is obtained at a point


Choose the correct alternative :

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


Choose the correct alternative :

The half plane represented by 4x + 3y ≥ 14 contains 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.


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


Maximize z = 10x + 25y subject to x + y ≤ 5, 0 ≤ x ≤ 3, 0 ≤ y ≤ 3


Minimize z = 7x + y subjected to 5x + y ≥ 5, x + y ≥ 3, 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


Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≥ 6, y ≥ 0 is this LPP solvable? Justify your answer.


State whether the following statement is True or False:

Objective function of LPP is a relation between the decision variables


Solve the following linear programming problems by graphical method.

Minimize Z = 3x1 + 2x2 subject to the constraints 5x1 + x2 ≥ 10; x1 + x2 ≥ 6; x1 + 4x2 ≥ 12 and x1, x2 ≥ 0.


Solve the following linear programming problems by graphical method.

Minimize Z = 20x1 + 40x2 subject to the constraints 36x1 + 6x2 ≥ 108; 3x1 + 12x2 ≥ 36; 20x1 + 10x2 ≥ 100 and x1, x2 ≥ 0.


A solution which maximizes or minimizes the given LPP is called


Solve the following linear programming problem graphically.

Maximise Z = 4x1 + x2 subject to the constraints x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 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 values of θ satisfying sin7θ = sin4θ - sinθ and 0 < θ < `pi/2` are ______


The minimum value of z = 5x + 13y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10, x ≥ 0, y ≥ 2 is ______ 


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


The set of feasible solutions of LPP is a ______.


Solve the following problems by graphical method:

Maximize z = 4x + 2y subject to 3x + y ≥ 27, x + y ≥ 21, x ≥ 0 y ≥ 0


Solve the following LPP by graphical method:

Maximize: z = 3x + 5y Subject to:  x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0


Food F1 contains 2, 6, 1 units and food F2 contains 1, 1, 3 units of proteins, carbohydrates, fats respectively per kg. 8, 12 and 9 units of proteins, carbohydrates and fats is the weekly minimum requirement for a person. The cost of food F1 is Rs. 85 and food F2 is Rs. 40 per kg. Formulate the L.P.P. to minimize the cost.


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