मराठी

In a LPP, the objective function is always ______. - Mathematics

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प्रश्न

In a LPP, the objective function is always ______.

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उत्तर

In a LPP, the objective function is always linear.

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पाठ 12: Linear Programming - Exercise [पृष्ठ २५७]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 12 Linear Programming
Exercise | Q 36 | पृष्ठ २५७

संबंधित प्रश्‍न

Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP


Solve the following Linear Programming Problems graphically:

Minimise Z = – 3x + 4 y

subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.


Solve the following Linear Programming Problems graphically:

Maximise Z = 5x + 3y

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


Solve the following Linear Programming Problems graphically:

Minimise Z = 3x + 5y

such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.


Show that the minimum of Z occurs at more than two points.

Minimise and Maximise Z = x + 2y 

subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.


Show that the minimum of Z occurs at more than two points.

Maximise Z = – x + 2y, Subject to the constraints:

x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.


Show that the minimum of Z occurs at more than two points.

Maximise Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.


A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per bag contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional elements A, 11.25 units of element B, and 3 units of element C. 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?


Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2, x ≥ 0, y ≥ 0.


Determine the maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure


Refer to quastion 12. What will be the minimum cost?


Refer to question 13. Solve the linear programming problem and determine the maximum profit to the manufacturer


Refer to question 15. Determine the maximum distance that the man can travel.


A company makes 3 model of calculators: A, B and C at factory I and factory II. The company has orders for at least 6400 calculators of model A, 4000 calculator of model B and 4800 calculator of model C. At factory I, 50 calculators of model A, 50 of model B and 30 of model C are made every day; at factory II, 40 calculators of model A, 20 of model B and 40 of model C are made everyday. It costs Rs 12000 and Rs 15000 each day to operate factory I and II, respectively. Find the number of days each factory should operate to minimise the operating costs and still meet the demand.


The feasible solution for a LPP is shown in Figure. Let Z = 3x – 4y be the objective function. Minimum of Z occurs at ______.


Refer to Question 27. Maximum of Z occurs at ______.


Refer to Question 27. (Maximum value of Z + Minimum value of Z) is equal to ______.


Refer to Question 30. Minimum value of F is ______.


Refer to Question 32, Maximum of F – Minimum of F = ______.


In a LPP, the linear inequalities or restrictions on the variables are called ____________.


In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same ______ value.


Objective function of a linear programming problem is ____________.


In linear programming infeasible solutions


A maximum or a minimum may not exist for a linear programming problem if ____________.


In Corner point method for solving a linear programming problem, one finds the feasible region of the linear programming problem, determines its corner points, and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, M is the maximum value of the objective function if ____________.


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If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum.


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Z = 6x + 21 y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at ____________.


The feasible region for an LPP is shown shaded in the figure. Let Z = 3x - 4y be the objective function. Minimum of Z occurs at ____________.


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