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In LPP with two variable, if m is the number of constraints and nonnegativity constraints x > 0, y > 0,
the feasible region in the graphical solution will be surrounded by how many lines?
the feasible region in the graphical solution will be surrounded by how many lines?
- a)m
- b)m + 1
- c)m - 2
- d)m + 2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In LPP with two variable, if m isthe number of constraints and nonnega...
≥ 0 and y ≥ 0 are included, then the standard form of the problem will have m constraints and 2+m variables. The objective function will have 2 variables (x and y) and the m constraints will be expressed in terms of x, y, and the slack variables s1, s2, ..., sm. Each constraint will have a nonnegativity constraint on its slack variable si ≥ 0.
The standard form of the problem can be written as:
Maximize (or minimize) z = ax + by
Subject to:
cx + dy + s1 = b1
ex + fy + s2 = b2
.
.
.
gx + hy + sm = bm
x ≥ 0, y ≥ 0, s1 ≥ 0, s2 ≥ 0, ..., sm ≥ 0
Here, a, b, c, d, e, f, g, and h are constants representing the coefficients of the variables in the objective function and constraints. The constants b1, b2, ..., bm represent the right-hand side of the constraints.
The variables x and y are the decision variables that we want to find the optimal values for. The slack variables s1, s2, ..., sm represent the amount by which the left-hand side of each constraint falls short of the right-hand side.
The nonnegativity constraints x ≥ 0 and y ≥ 0 ensure that the decision variables are always positive or zero, while the nonnegativity constraints on the slack variables s1 ≥ 0, s2 ≥ 0, ..., sm ≥ 0 ensure that the left-hand side of each constraint is always greater than or equal to the right-hand side.
The standard form of the problem can be written as:
Maximize (or minimize) z = ax + by
Subject to:
cx + dy + s1 = b1
ex + fy + s2 = b2
.
.
.
gx + hy + sm = bm
x ≥ 0, y ≥ 0, s1 ≥ 0, s2 ≥ 0, ..., sm ≥ 0
Here, a, b, c, d, e, f, g, and h are constants representing the coefficients of the variables in the objective function and constraints. The constants b1, b2, ..., bm represent the right-hand side of the constraints.
The variables x and y are the decision variables that we want to find the optimal values for. The slack variables s1, s2, ..., sm represent the amount by which the left-hand side of each constraint falls short of the right-hand side.
The nonnegativity constraints x ≥ 0 and y ≥ 0 ensure that the decision variables are always positive or zero, while the nonnegativity constraints on the slack variables s1 ≥ 0, s2 ≥ 0, ..., sm ≥ 0 ensure that the left-hand side of each constraint is always greater than or equal to the right-hand side.
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In LPP with two variable, if m isthe number of constraints and nonnegativityconstraints x > 0, y > 0,the feasible region in the graphicalsolution will be surrounded by howmany lines?a)mb)m + 1c)m - 2d)m + 2Correct answer is option 'D'. Can you explain this answer?
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