Question

Each constraint in a linear programming model must contain the equality sign (“<=”, “>=”, or “=”).

Select one:

True

False

Answer #1

**Answer: True**

**Explanation:**

While solving the linear programing problem it is neccessay to have equality (=) constraints.

Since only equality
constraints are treated in standard linear programming, the
inequalities *A***x** ≤ **b** or
*A***x** ≥ **b** must be converted
to equalities.But the constraints like *A***x**
< **b** or *A***x** >
**b can not be** converted to equalities.

**Hence Each constraint in a
linear programming model must contain the equality sign (“<=”,
“>=”, or “=”). This is True**

Consider the following linear programming model with 4 regular
constraints: Maximize 3X + 5Y subject to: 4X + 4Y ≤ 48 (constraint
#1) 2X + 3Y ≤ 50 (constraint #2) 1X + 2Y ≤ 20 (constraint #3) Y ≥ 2
(constraint #4) X, Y ≥ 0 (non-negativity constraints) (a) Which of
the constraints is redundant? Constraint #____. Justify using the
data from the above LP model:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
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The following is the mathematical model of a linear programming
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Maximize Z = 2X1 + 3X2
subject to:
4X1 + 9X2 ≤ 72
10X1 + 11X2 ≤ 110
17X1 + 9X2 ≤ 153
X1 , X2 ≥ 0
The constraint lines have been graphed below along with one example
profit line (dashed). The decision variable X1 is used as the X
axis of the graph.
Which of the following gives the constraint line that cuts the
X2...

Consider the following linear programming model
MAX 100 C + 80 S
C <= 20
S - C >= 10
C , S >= 0
The feasible region is shaded. At the optimal solution, the
objective function value is 5,200
What is the maximum allowable increase in the RHS of the
constraint
C <= 20 ?

If a problem is referred to as a linear programming problem,
what must be true?
A) the objective function must be
linear
B) both the objective function and the
constraints must be linear
C) the constraints must be linear
D) the decision variables must be
linear
Three essential elements of a linear programming formulation
are the:
A) decision variables, feasibility,
constraints
B) constraints, objective function,
non-negativity
C) decision variables, objective
function, constraints
D) objective function, constraints,
solution
When constraints identify...

** Linear Programming
**
Max Z = 6x1 +
10x2+9x3 + 20x4
constraint
4x1 + 9x2 + 7x3 + 10x4
= 600
x1 + x2+3x3 + 40x4=
400
3x1 + 4x2 + 2x3 + x4 =
500
x1,x2,x3 ,x4 ≥ 0
Find the allowable decrease
and increase for x4.

1) Constraints limit the degree to which the objective can be
pushed in linear programming. As a manager, how do you know which
constraints are proper to use in your decision model? Describe a
basic situation and give an example of a constraint you are able to
identify.
2) What role does feasibility play in linear programming, in
your opinion?

Solve the following linear programming model by using the
graphical method: graph the constraints and identify the feasible
region. Using the corner points method, determine the optimal
solution (s) (show your work).
Maximize Z = 6.5x1 + 10x2
Subject to x1 + x2 ≤ 15
2x1 + 4x2 ≤ 40
x1 ≥ 8
x1, x2 ≥ 0
b. If the constraint x1 ≥ 8 is changed to x1 ≤ 8, what effect
does this have on the optimal solution? Are...

1. What type of mathematical description can NOT refer to the
linear regression model
Select one or more:
a. a linear equation
b. a sytem of linear equations
c. a collection of random variables
d. a sytem of an equation and inequalities
2. Linear regression is the most complicated form of
regression.
Select one:
True
False
3. What type of regression is this?
Fast and easy to model and is particularly useful when the
relationship to be modeled is not...

Suppose that in a linear programming model, all resources have
been paid for. Then at the optimal solution the shadow price (dual
value) represents
The minimum amount you would pay for one more unit of
resource
The maximum amount you would pay for one more unit of
resource
The exact amount you would pay for one more unit of resource
The cost of one more unit of resource
None of the above

Why does a linear programming model require an objective
function and constraints? Why do we need to do sensitivity analysis
in solving a linear optimization problem?

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