### Class XII

Maximize Z = 50x+60y , subject to constraints x +2 y ≤ 50 , x +y ≥ 30, x, y ≥ 0.
1. 2500
2. 1600
3. 1547
4. 1525
In linear programming infeasible solutions
1. fall inside the a regular polygon
2. fall inside the feasible region
3. fall on the x = 0 plane
4. fall outside the feasible region
A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?
1. 8 Souvenir of types A and 20 of Souvenir of type B; Maximum profit = Rs 160
2. 8 Souvenir of types A and 27 of Souvenir of type B; Maximum profit = Rs 170
3. 9 Souvenir of types A and 21 of Souvenir of type B; Maximum profit = Rs 163
4. 7 Souvenir of types A and 210 of Souvenir of type B; Maximum profit = Rs 161
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
If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum.
1. then any point on the line segment joining these two points is also an optimal solution of the opposite type
2. then no point on the line segment joining these two points is an optimal solution of thesame type
3. then any point on the line segment joining these two points is also an optimal solution of the same type
4. then no point on the line segment joining these two points is an optimal solution of the opposite type
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