Linear Programming

Subject matter experts of JagranJosh have developed chapter wise practice questions of Class 12th as per the relevancy of the chapter in the CBSE board exam. This practice set contains 10 questions with detailed explanations on “Chapter: Linear Programming” of Mathematics.

  • Q1.A cooperative society of farmers has 50 hectares of land to grow two crops A and B. The profits from crops A and B per hectare are estimated as Rs 10,500 and Rs 9.000 respectively. To control weeds, a liquid herbicide has to be used for crops A and B at the rate of 20 litres and 10 litres per hectare, respectively. Further not more than 800 litres of herbicide should be used in order to protect fish and wildlife using a pond which collects drainage from this land. Keeping in mind that the protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each crop so as to maximize the total profit? Form an LPP from the above and solve it graphically. Which of the following is true?

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  • Q2.The feasible solution for a LPP is shown in Fig.. Let Z = 3x - 4y be the objective function. Minimum of Z occurs at

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  • Q3.The maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in figure is:

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  • Q4.The common region determined by all the linear constraints of a LPP is/are called :

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  • Q5.In a LPP, the linear function which has to be maximised or minimised is called

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  • Q6.The feasible region for an LPP is always a:

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  • Q7.The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 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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