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प्रश्न
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.
विकल्प
True
False
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उत्तर
This statement is True.
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संबंधित प्रश्न
Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 4y
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Solve the following Linear Programming Problems graphically:
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Solve the following Linear Programming Problems graphically:
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Show that the minimum of Z occurs at more than two points.
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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?
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?
It is being given that at least one of each must be produced.
To maintain his health a person must fulfil certain minimum daily requirements for several kinds of nutrients. Assuming that there are only three kinds of nutrients-calcium, protein and calories and the person's diet consists of only two food items, I and II, whose price and nutrient contents are shown in the table below:
| Food I (per lb) |
Food II (per lb) |
Minimum daily requirement for the nutrient |
||||
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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
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In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.
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 14. How many sweaters of each type should the company make in a day to get a maximum profit? What is the maximum profit.
Refer to question 15. Determine the maximum distance that the man can travel.
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.
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Refer to Question 30. Minimum value of F is ______.
Refer to Question 32, Maximum of F – Minimum of F = ______.
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The feasible region for an LPP is always a ______ polygon.
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Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
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.
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Minimize Z = 30x + 50y
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In linear programming infeasible solutions
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