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Solve the linear programming problem.Maximise z = x + 2y, subject to constraints x – y ≤ 10 , 2x + 3y ≤ 20 and x ≥ 0 , y ≥ 0.

1) z = 10 2) z = 30 3) z = 40 4) z = 50 5) None of the above Solution: (5) None of the above z = x + 2y Subject to constraints, x - y ≤ 10,... View Article

The feasible region for the following constraints L₁ ≤ 0, L₂ ≥ 0, L₃ = 0, x ≥ 0, y ≥ 0 in the diagram shown is

1) area DHF 2) area AHC 3) line segment EG 4) line segment GI 5) line segment IC Solution: (3) line segment EG The feasible region for... View Article

Maximum value of z = 3x + 4y subject to constraints x – y ≤ -1, -x + y ≤ 0 and x , y ≥ 0, is given by

1) 1 2) 4 3) 6 4) no feasible region Solution: (4) no feasible region There is no common point or no common feasible area.... View Article

The coordinate of the point at which minimum value of z = 7x – 8y subject to constraints x + y – 20 ≤ 0, y ≥ 5, x ≥ 0, y ≥ 0 is attained, is

1) (20, 0) 2) (15, 5) 3) (0, 5) 4) (0, 20) Solution: (4) (0, 20) z = 7x - 8y Subject to constraints x + y - 20 ≤ 0, y ≥ 5, x ≥ 0, y ≥ 0... View Article

Shaded region is represented by

1) 4x - 2y ≤ 3 2) 4x - 2y ≤ - 3 3) 4x - 2y ≥ 3 4) 4x - 2y ≥ - 3 Solution: (2) 4x - 2y ≤ - 3 The shaded region represents 4x - 2y ≤ - 3.... View Article

The minimum value of the objective function Z = 2x + 10y subject to constraints x ≥ 0, y ≥ 0, x – y ≥ 0, x – 5y ≤ – 5 is

1) 10 2) 15 3) 12 4) 8 Solution: (2) 15 Z = 2x + 10y Subject to constraints x ≥ 0, y ≥ 0, x - y ≥ 0, x - 5y ≤ - 5 The region required is... View Article

If given constraints are 5x + 4y ≥ 2 , x ≤ 6 and y ≤ 7, then the maximum value of the function Z = x + 2y is

1) 13 2) 14 3) 15 4) 20 Solution: (4) 20 z = x + 2y and 5x + 4y = 2 (x / (2 / 5)) + (y / (1 / 2)) = 1 At A (2 / 5, 0), Z = 2 / 5 At B... View Article

The maximum value of Z is where, Z = 4x + 2y subject to constraints 4x + 2y ≥ 46 , x + 3y ≤ 24 and x, y ≥ 0, is

1) 46 2) 96 3) 52 4) None of these Solution: (2) 96 Z = 4x + 2y Subject to constraints 4x + 2y ≥ 46 , 2x + y ≥ 23 x 0... View Article

The maximum value of Z = 4x + 2y subject to constraints 2x + 3y ≤ 18 , x + y ≥ 10 and x , y ≥ 0 is

1) 20 2) 36 3) 40 4) None of these Solution: (4) None of these Z = 4x + 2y Subject to constraints 2x + 3y ≤ 18, x + y ≥ 10 and x , y ≥ 0... View Article

Which of the term is not used in a linear programming problem?

1) Optimal solution 2) Feasible solution 3) Concave region 4) Objective function Solution: (3) Concave region The term concave region is not... View Article

The constraints -x₁ + x₂ ≤ 1, -x₁ + 3x₂ ≤ 9 and x₁, x₂ ≥ 0 defines on

1) bounded feasible space 2) unbounded feasible space 3) both bounded and unbounded feasible space 4) None of the above Solution: (2)... View Article

The maximum value of Z = 5x + 3y, subject to constraints 3x + 5y ≤ 15, 5x + 2y ≤ 10 and x , y ≥ 0 is

1) 235 / 19 2) 325 / 19 3) 523 / 19 4) 532 / 19 Solution: (1) 235 / 19 Z = 5x + 3y Subject to constraints 3x + 5y ≤ 15, x... View Article

If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0 then c is equal to

1) 1 2) - 1 3) 3 4) - 3 Solution: Given 6x2 - xy + 4cy2 = 0…(i) One of the line is 3x + 4y = 0 So (3x + 4y)(2x + cy) = 0 6x2 + 8xy + 3cxy +... View Article

The straight lines 3x + 4y – 5 = 0 and 4x – 3y = 15 intersected at the point P. On these lines, the points Q and R are chosen so that PQ = PR. The slopes of the line QR passing through (1, 2) are

1) -7, 1/7 2) 7, 1/7 3) 7, (-1/7) 4) 3, -(1/3) Solution: Given lines are 3x + 4y - 5 = 0…(i) 4x = 3y + 15…(ii) Slope of (i) m1 = -¾ Slope of... View Article

A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 and makes equal intercepts with axes. Then, equation of the line is

1) 5x + 5y - 3 = 0 2) x + 5y - 3 = 0 3) 5x - y - 3 = 0 4) 5x + 5y + 3 = 0 Solution: Given 3x + y + 1 = 0 ..(i) 2x - y + 3 = 0 …(ii) Solving... View Article