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Corner points of the feasible region determined by the system of linear constraints are 0,3, 1,1 and 3,0. Let Z=px+qy, where p, q>0. Condition on p and q so that the minimum of Z occurs at 3,0 and 1,1 is

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Important Questions on Linear Programming

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The corner points of the feasible region determined by the system of linear constraints are 0,10,5,515,15,0,20. Let Z=px+qy, where p, q>0. Condition on p and q so that the maximum of Z occurs at both the points 15,15 and 0,20 is
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The region represented by the inequalities x6, y2, 2x+y10, x0, y0 is
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Let Z=7x+y subjected to 5x+y5, x+y3, x0, y0. The minimum value of Z occurs at
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The solution set of the following system of inequations x+2y3, 3x+4y12, x0, y1, is
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Linear inequalities for which the shaded region of the given figure is the solution set, are

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There is a factory located at each of the two places P and Q. From these locations, a certain commodity is delivered to each of the three depots situated at A,B and C. The weekly requirements of the depots are respectively, 5, 5 and 4 units commodity, while the production capacity of the factories at P and Q are 8 and 6 units, respectively. The cost of transportation per unit is given below:

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Formulate the L.P.P., so that the units transported from each factory to each depot in such an order that the transportation cost is minimum.

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A farmer mixes two brands P and Q of cattle feed. Brand P, costing  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 200 per bag contains 1.5 units of nutritional element A, 11.25  units of elements 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. Then, the minimum cost is
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A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each. The cost for engaging each large van is 400 and each small van is 200. Not more than 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans. Then, the minimum cost for the firm is