हिंदी

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

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प्रश्न

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

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उत्तर

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

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अध्याय 12: Linear Programming - Exercise [पृष्ठ २५७]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 12 Linear Programming
Exercise | Q 35 | पृष्ठ २५७

वीडियो ट्यूटोरियलVIEW ALL [2]

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:

Maximise Z = 3x + 4y

subject to the constraints : x + y ≤ 4, 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.


Solve the following Linear Programming Problems graphically:

Minimise Z = x + 2y

subject to 2x + y ≥ 3, x + 2y ≥ 6, 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.


Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?


A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin content of one kg food is given below:

Food Vitamin A Vitamin B Vitamin C
X 1 2 3
Y 2 2 1

One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?

 


A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Type of toy Machines
I II III
A 12 18 6
B 6 0 9

Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

 


An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?


The minimum value of the objective function Z = ax + by in a linear programming problem always occurs at only one corner point of the feasible region


Determine the maximum value of Z = 11x + 7y subject to the constraints : 2x + y ≤ 6, x ≤ 2, x ≥ 0, y ≥ 0.


Refer to Exercise 7 above. Find the maximum value of Z.


In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.


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


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 corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y ______.

Compare the quantity in Column A and Column B

Column A Column B
Maximum of Z 325

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 30. Minimum value of F is ______.


Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. The Minimum value of F occurs at  ______.


If the feasible region for a LPP is ______ then the optimal value of the objective function Z = ax + by may or may not exist.


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.


A corner point of a feasible region is a point in the region which is the ______ of two boundary lines.


If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.


In a LPP, the minimum value of the objective function Z = ax + by is always 0 if the origin is one of the corner point of the feasible region.


The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x - 2y ≥ 0, x ≥ 0, y ≥ 0 is ____________.


Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at ____________.


In linear programming infeasible solutions


Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.


Maximize Z = 10 x1 + 25 x2, subject to 0 ≤ x1 ≤ 3, 0 ≤ x2 ≤ 3, x1 + x2 ≤ 5.


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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