### Class XII

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. If M and m respectively be the largest and smallest values at corner points then
1. If the feasible region is unbounded, M and m respectively are the maximumand minimum values of the objective function
2. None of these
3. If the feasible region is bounded, M and m respectively are the minimum and maximum values of the objective function
4. If the feasible region is bounded, M and m respectively are the maximum and minimum values of the objective function
There are two types of fertilizers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Rs 6/kg and F2 costsRs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
1. 120 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1200
2. 130 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1300
3. 110 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1100
4. 100 kg of fertilizer F1 and 80 kg of fertilizer F2; Minimum cost = Rs 1000
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?
1. 3 packages of nuts and 4 packages of bolts; Maximum profit = Rs 74.50.
2. 3 packages of nuts and 3 packages of bolts; Maximum profit = Rs 73.50.
3. 4 packages of nuts and 3 packages of bolts; Maximum profit = Rs 75.50.
4. 4 packages of nuts and 4 packages of bolts; Maximum profit = Rs 76.50.
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
1. any point on the line segment joining the points (0, 2) and (3, 0).
2. the mid – point of the line segment joining the points (0, 2) and (3, 0) only
3. (0, 2) only
4. (3, 0) only
A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
1. 800 dolls of type A and 400 dolls of type B; Maximum profit = Rs 16000
2. 820 dolls of type A and 420 dolls of type B; Maximum profit = Rs 16200
3. 840 dolls of type A and 404 dolls of type B; Maximum profit = Rs 16500
4. 830 dolls of type A and 430 dolls of type B; Maximum profit = Rs 16300
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