In a test of Mathematics, there are two types of questions to be answered?short answered and long answered. The relevant data is given below
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Linear Programming  ETEA Model Test MCQS  Part  VI
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A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter requires 3 hour each and in manufacturing of product B, the machine and carpenter requires 5 hour and 3 hour respectively. The machine and carpenter work at most 80 hour and 50 hour per week respectively. The profit on A and B is Rs. 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then for the function $6x+8y$ the constraints are0$x\ge 0,\ y\ge 0,\ 5x+3y\le 80,\ 3x+2y\le 50$0%0$x\ge 0,\ y\ge 0,\ 3x+5y\le 80,\ 3x+3y\le 50$0%0$x\ge 0,\ y\ge 0,\ 3x+5y\ge 80,\ 2x+3y\ge 50$0%0$x\ge 0,\ y\ge 0,\ 5x+3y\ge 80,\ 3x+2y\ge 50$0%0
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A shopkeeper wants to purchase two articles A and B of cost price Rs. 4 and 3 respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total article worth more than Rs. 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are0$x\ge 0,\ y\ge 0,\ 4x+3y\le 24$0%0$x\ge 0,\ y\ge 0,\ 30x+10y\le 24$0%0$x\ge 0,\ y\ge 0,\ 4x+3y\ge 24$0%0$x\ge 0,\ y\ge 0,\ 30x+40y\ge 24$0%0
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The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is x and second number y, then for maximizing the product of these two numbers, the mathematical formulation is0$x+y\ge 5$ , $2yx\ge 4,\ \ x\ge 0,\ y\ge 0$0%0$x+y\ge 5$ , $2x+y\ge 4,\ \ x\ge 0,\ y\ge 0$0%0$x+y\le 5$ , $2yx\le 4,\ \ x\ge 0,\ y\ge 0$0%0None of these0%0
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