True or False Questions 1. For an LP with m inequality constraints and n decisio
ID: 445751 • Letter: T
Question
True or False Questions
1. For an LP with m inequality constraints and n decision variables, its standard form consists of m equality constraints and (m+n) decision variables.
2. For an LP with m inequality constraints and n decision variables, a basic feasible solution to the LP has m basic variables andn nonbasic variables.
3. For an LP with m equality constraints and n decision variables, if n > m, a basic feasible solution to the LP has (n – m) basic variables and m nonbasic variables.
4. A basic feasible solution to an LP corresponds to an extreme point in its feasible region.
LP Multiple Choice Problem
max z = x1 + 3x2
s.t. x1 + 2x2 6
2x1 + x2 8
x1, x2 0
For the LP above, which of the following is its standard form?
a.
max z = x1 + 3x2
s.t. x1 + 2x2 + s1 = 6
2x1 + x2 + s2 = 8
x1, x2, s1, s2 0
b.
max z = x1 + 3x2
s.t. x1 + 2x2 – e1 = 6
2x1 + x2 – e2 = 8
x1, x2, e1, e2 0
c.
max z = x1 + 3x2
s.t. x1 + 2x2 + s1 = 6
2x1 + x2 – e2 = 8
x1, x2, s1, e2 0
d.
max z = x1 + 3x2
s.t. x1 + 2x2 – e1 = 6
2x1 + x2 + s2 = 8
x1, x2, e1, s2 0
max z = x1 + 3x2
s.t. x1 + 2x2 + s1 = 6
2x1 + x2 + s2 = 8
x1, x2, s1, s2 0
b.
max z = x1 + 3x2
s.t. x1 + 2x2 – e1 = 6
2x1 + x2 – e2 = 8
x1, x2, e1, e2 0
c.
max z = x1 + 3x2
s.t. x1 + 2x2 + s1 = 6
2x1 + x2 – e2 = 8
x1, x2, s1, e2 0
d.
max z = x1 + 3x2
s.t. x1 + 2x2 – e1 = 6
2x1 + x2 + s2 = 8
x1, x2, e1, s2 0
Explanation / Answer
1. For an LP with m inequality constraints and n decision variables, its standard form consists of m equality constraints and (m+n) decision variables. TRUE
2.For an LP with m inequality constraints and n decision variables, a basic feasible solution to the LP has m basic variables andn nonbasic variables. FALSE
3.For an LP with m equality constraints and n decision variables, if n > m, a basic feasible solution to the LP has (n – m) basic variables and m nonbasic variables. TRUE
4.D.max z = x1 + 3x2
s.t. x1 + 2x2 – e1 = 6
2x1 + x2 + s2 = 8
x1, x2, e1, s2 0
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