Two linear programming problems (LPPs) have same bounded feasible region with three corner points $(0, 3), (4, 4), (7, 0)$. If $Z_1 = x - 3y$ and $Z_2 = 2x + y$ are objective functions of LPPs, then which of the following is/are correct?

A. only $Z_1$ maximizes at $(7, 0)$.

B. both $Z_1, Z_2$ minimize at $(0, 3)$.

C. both $Z_1, Z_2$ maximize at $(7, 0)$.

D. $Z_2$ maximizes at $(4, 4)$.

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Which of the following terms are associated with a linear programming problem?

(A) Constraints

(B) Independent events

(C) Feasible region

(D) Objective function

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The feasible region for a linear programming problem is shown in the figure.

Let $Z = 3x - 4y$ be the objective function, then minimum of Z occurs at the point

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0,0)$, $(4,0)$, $(2,4)$ and $(0,5)$. If maximum value of $z = ax + by$, where $a,b > 0$, occurs at both $(2,4)$ and $(4,0)$ then

The corner points of the feasible region associated with the LPP: Maximise $Z = px + qy$, $p,q > 0$ subject to $2x + y \leq 10$, $x + 3y \leq 15$, $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$, $(0, 40)$, $(20, 40)$, $(60, 20)$, $(60, 0)$. If the objective function is $z = 4x + 3y$, then which one of the following is true?

Match List-I with List-II

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