CUET-PG 2023 Shift 1 Question 43: Constrained optimisation and linear programming
A general linear programming problem which is a maximization problem in two decision variables (x1 and x2) and two resource constraints (b1 and b2) can be set up in the following way:
(A) Specify the inequality constraints also known as the resource constraints as a11x1+a12x2≤b1 and a21x1+a22x2≤b2; and non-negativity constraints: x1≥0,x2≥0.
(B) Solve the problem and plot the constraints on a graph in (x1,x2) space to define the feasible solution.
(C) Specify the criterion function which involves maximizing a linear function: maxz=c1x1+c2x2.
(D) The optimal solutions given by (x1∗,x2∗) can be used to find the maximum value of the objective function z∗.
Choose the correct answer from the options given below:
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A general linear programming problem which is a maximization problem in two decision variables (x1 and x2) and two resource constraints (b1 and b2) can be set up in the following way: (A) Specify the inequality constraints also known as the resource constraints as a₁₁x₁+a₁₂x₂≤ b₁ and a₂₁x₁+a₂₂x₂≤ b₂; and non-negativity constraints: x₁≥0, x₂≥0. (B) Solve the problem and plot the constraints on a graph in (x₁, x₂) space to define the feasible solution. (C) Specify the criterion function which involves maximizing a linear function: max z = c₁x₁+c₂x₂. (D) The optimal solutions given by (x₁*, x₂*) can be used to find the maximum value of the objective function z*. Choose the correct answer from the options given below: (A) D, A, B, C (B) C, A, B, D (C) C, B, D, A (D) D, C, B, A
Also written as: A general linear programming problem which is a maximization problem in two decision variables (x1 and x2) and two resource constraints (b1 and b2) can be set up in the following way: (A) Specify the inequality constraints also known as the resource constraints as a_(11)x_1+a_(12)x_2<= b_1 and a_(21)x_1+a_(22)x_2<= b_2; and non-negativity constraints: x_1>=0, x_2>=0. (B) Solve the problem and plot the constraints on a graph in (x_1, x_2) space to define the feasible solution. (C) Specify the criterion function which involves maximizing a linear function: max z = c_1x_1+c_2x_2. (D) The optimal solutions given by (x_1*, x_2*) can be used to find the maximum value of the objective function z*. Choose the correct answer from the options given below:
Constrained optimisation and linear programming has come up 44 times in 7 exams since 2007.
What this question tests
This question is on Linear programming: formulation and graphical solution, part of Constrained optimisation and linear programming in Mathematics.
Setting up a linear program and finding its optimum at a corner of the feasible region.
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