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

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प्रश्न

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

विकल्प

  • True

  • False

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उत्तर

This statement is True.

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अध्याय 12: Linear Programming - Exercise [पृष्ठ २५७]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 12 Linear Programming
Exercise | Q 42 | पृष्ठ २५७

संबंधित प्रश्न

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 = 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.

Minimise and Maximise Z = x + 2y 

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

 


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?


If the feasible region for a linear programming problem is bounded, then the objective function Z = ax + by has both a maximum and a minimum value on R.


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


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


The feasible region for a LPP is shown in Figure. Find the minimum value of Z = 11x + 7y


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


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


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  ______.


In a LPP, the objective function is always ______.


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.


The feasible region for an LPP is always a ______ polygon.


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.


In a LPP, the maximum value of the objective function Z = ax + by is always finite.


A linear programming problem is as follows:

Minimize Z = 30x + 50y

Subject to the constraints: 3x + 5y ≥ 15, 2x + 3y ≤ 18, x ≥ 0, y ≥ 0

In the feasible region, the minimum value of Z occurs at:


Objective function of a linear programming problem is ____________.


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 ____________.


A linear programming problem is one that is concerned with ____________.


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 ____________.


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


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


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 ____________.


Maximize Z = 10×1 + 25×2, subject to 0 ≤ x1 ≤ 3, 0 ≤ x2 ≤ 3, x1 + x2 ≤ 5.


The feasible region for an LPP is shown shaded in the following figure. Minimum of Z = 4x + 3y occurs at the point.


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