COB 291 GRADED APLUS QUESTION
COLLECTION WITH DETAILED SOLUTION
COVERAGE
●● When is Linear Programming used?
Answer: LP is used when we have a set of decision variables
(controllable inputs)
●● What is the goal of Linear Programming?
Answer: To find the best values of the decision variables to achieve max
profit or min cost
●● 5 Steps in Formulating LP Models
Answer: 1. Understand the problem.
2. Identify the decision variables.
3. State the objective function as a linear
combination of the decision variables.
4. State the constraints as linear combinations of the
decision variables.
5. Identify any upper or lower bounds on the
decision variables.
,●● constraints
Answer: restrictions placed on potential solutions to a problem
●● objective function
Answer: The function being maximized or minimized in Linear
Programming
●● objective function coefficients
Answer: represent the marginal profits (or costs) associated with the
decision variables.
●● Feasible Solution
Answer: A solution point that satisfies all the constraints simultaneously.
●● Infeasible Solution
Answer: A decision alternative or solution that does not satisfy one or
more constraints.
●● optimal solution
Answer: The feasible solution that provides the best possible value of
the objective function.
●● Optimal Objective Function Value
, Answer: In a maximization (minimization) problem, the optimal value is
the least upper (largest lower) bound of the objective function values
over the entire feasible solutions.
●● Three Assumptions of Linear Programming Models
Answer: Proportionality: contribution to the objective function and the
amount of resources used in each constraint is a proportional value of
each decision variable
Additivity: The value of the objective function and total resources used
can be found by summing the objective function contribution and the
resources used for all decision variables.
Divisibility: the decision variables are continuous.
●● Solving LP graphically
Answer: - An LP problem involving only two decision variables (like 𝑥
and 𝑦) can be solved using a graphical solution procedure.
- Horizontal axis represents one decision variable (𝑥), and vertical axis
represents the other decision variable (𝑦).
- Any point on the graph shows a combination of 𝑥 and 𝑦, so it can be a
possible solution.
- 𝑥=0 and 𝑦=0 is the origin
●● Corner Point
Answer: a point in the feasible region where two or more of the
boundary lines of the constraints intersect.
COLLECTION WITH DETAILED SOLUTION
COVERAGE
●● When is Linear Programming used?
Answer: LP is used when we have a set of decision variables
(controllable inputs)
●● What is the goal of Linear Programming?
Answer: To find the best values of the decision variables to achieve max
profit or min cost
●● 5 Steps in Formulating LP Models
Answer: 1. Understand the problem.
2. Identify the decision variables.
3. State the objective function as a linear
combination of the decision variables.
4. State the constraints as linear combinations of the
decision variables.
5. Identify any upper or lower bounds on the
decision variables.
,●● constraints
Answer: restrictions placed on potential solutions to a problem
●● objective function
Answer: The function being maximized or minimized in Linear
Programming
●● objective function coefficients
Answer: represent the marginal profits (or costs) associated with the
decision variables.
●● Feasible Solution
Answer: A solution point that satisfies all the constraints simultaneously.
●● Infeasible Solution
Answer: A decision alternative or solution that does not satisfy one or
more constraints.
●● optimal solution
Answer: The feasible solution that provides the best possible value of
the objective function.
●● Optimal Objective Function Value
, Answer: In a maximization (minimization) problem, the optimal value is
the least upper (largest lower) bound of the objective function values
over the entire feasible solutions.
●● Three Assumptions of Linear Programming Models
Answer: Proportionality: contribution to the objective function and the
amount of resources used in each constraint is a proportional value of
each decision variable
Additivity: The value of the objective function and total resources used
can be found by summing the objective function contribution and the
resources used for all decision variables.
Divisibility: the decision variables are continuous.
●● Solving LP graphically
Answer: - An LP problem involving only two decision variables (like 𝑥
and 𝑦) can be solved using a graphical solution procedure.
- Horizontal axis represents one decision variable (𝑥), and vertical axis
represents the other decision variable (𝑦).
- Any point on the graph shows a combination of 𝑥 and 𝑦, so it can be a
possible solution.
- 𝑥=0 and 𝑦=0 is the origin
●● Corner Point
Answer: a point in the feasible region where two or more of the
boundary lines of the constraints intersect.
