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

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प्रश्न

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

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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 45 | पृष्ठ २५७

संबंधित प्रश्न

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 = 5x + 10 y

subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 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?


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


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


Feasible region (shaded) for a LPP is shown in Figure. Maximise Z = 5x + 7y.


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


Refer to question 14. How many sweaters of each type should the company make in a day to get a maximum profit? What is the maximum profit.


A manufacturer produces two Models of bikes-Model X and Model Y. Model X takes a 6 man-hours to make per unit, while Model Y takes 10 man-hours per unit. There is a total of 450 man-hour available per week. Handling and Marketing costs are Rs 2000 and Rs 1000 per unit for Models X and Y respectively. The total funds available for these purposes are Rs 80,000 per week. Profits per unit for Models X and Y are Rs 1000 and Rs 500, respectively. How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Find the maximum profit.


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


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


The feasible region for an LPP is shown in the figure. Let F = 3x – 4y be the objective function. Maximum 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 linear inequalities or restrictions on the variables are called ____________.


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.


Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?


In the given graph, the feasible region for an LPP is shaded. The objective function Z = 2x – 3y will be minimum at:


For an objective function Z = ax + by, where a, b > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:


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


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


In linear programming, optimal solution ____________.


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


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