Question 1

All linear programming problems with only two variables may be solved using graphical method.

Accepted Answer

Graphical methods can solve linear programming problems with two variables by plotting the constraints and objective function on a graph to find the optimal solution.

Question 2

All linear programming problems with only two variables and a maximum of 10 constraints may be solved using graphical method.

Accepted Answer

False

Question 3

If a linear programming problem has redundant constraints, then the optimal solution without the redundant constraints will be the same as the optimal solution with the redundant constraints.

Accepted Answer

Redundant constraints do not affect the feasible region or the optimal solution of a linear programming problem; they are essentially extra information that does not change the outcome.

Question 4

If a linear program has a feasible solution with unbounded objective function value, then it must be an unbounded problem.

Accepted Answer

The answer of If a linear program has a feasible...

Question 5

If a graphically solvable linear program is unbounded, then the feasible region must be open at least in one direction.

Accepted Answer

In a graphically solvable linear program, if the feasible region is unbounded, it means that it extends infinitely in at least one direction, indicating that it is open in that direction.

Question 6

If a graphically solvable linear program is infeasible, that implies there is no point in the graph satisfying all constraints.

Accepted Answer

Infeasibility in a graphically solvable linear program means that the constraints of the program do not overlap to form a feasible region, indicating there is no point that simultaneously satisfies all constraints.

Question 7

If a graphically solvable linear program has multiple optimal solutions, it implies that two or more corner points are optimal.

Accepted Answer

In a graphically solvable linear program, if there are multiple optimal solutions, it means that the objective function line is parallel to one of the constraints in the feasible region, making all points along the edge connecting two or more corner points optimal as well.

Question 8

In any graphically solvable linear program, no point other than one of the corner points of the feasible region can ever be optimal.

Accepted Answer

The answer of In any graphically solvable linear program, no...

Question 9

In any graphically solvable linear program, it is enough if we examine all the corner points of the feasible region to find an optimal solution.

Accepted Answer

In a graphically solvable linear program, the optimal solution (if it exists) will always occur at one or more of the corner points (vertices) of the feasible region due to the linear nature of both the objective function and the constraints.

Question 10

In any graphically solvable linear program, if two points are feasible, then any weighted average of the two points (where weights are non-negative and add up to 1.0) will also be feasible.

Accepted Answer

This statement is true due to the convexity property of the feasible region in linear programming. The feasible region of a linear program is always a convex set, meaning that if two points are feasible, any convex combination (or weighted average where weights are non-negative and sum up to 1) of these points will also be within the feasible region, thus also being feasible.

Question 11

If a graphically solvable linear program is unbounded, then it can always be converted to a regular bounded problem by removing a constraint.

Accepted Answer

Removing a constraint from an unbounded linear program does not guarantee that the problem will become bounded; it may still remain unbounded or the solution space could change significantly, affecting feasibility and optimality.

Question 12

In a graphically solvable linear program, if one of the constraints is changed from " $\leq$ type" to "= type", all other things remaining the same, then the optimal solution will never change.

Accepted Answer

Changing a constraint from "$\leq$" to "=" type can potentially reduce the feasible region to a smaller set or even a single point, which might not include the previous optimal solution, thus potentially changing the optimal solution.

Question 13

In a graphically solvable linear program, if one of the constraints is changed from " $\leq$ type" to "= type", all other things remaining the same, the problem may become infeasible.

Accepted Answer

Changing a constraint from "$\leq$" to "=" in a linear program can restrict the feasible region to a smaller set or even a single point, and if this new constraint does not intersect the previously feasible region, the problem may become infeasible.

Question 14

In a graphically solvable linear program with an optimal solution, if one of the constraints is changed from "= type" to " $\leq$ type", all other things remaining the same, the problem may become infeasible.

Accepted Answer

Changing a constraint from "=" to "≤" type in a linear program expands the feasible region rather than shrinking it, making it less likely to become infeasible, as it allows for more solutions to satisfy the constraint.

Question 15

In a graphically solvable linear program with an optimal solution, if one of the constraints is changed from "= type" to " $\geq$ type", all other things remaining the same, the problem may become infeasible.

Accepted Answer

Changing a constraint from "= type" to "≥ type" in a linear program broadens the feasible region rather than narrowing it, making the problem not more likely to become infeasible but potentially altering the optimal solution or making the solution space larger.

Question 16

Assumptions of linear programming include
A) linearity
B) additivity
C) divisibility
D) certainty
E) all of the above

Accepted Answer

Linear programming assumptions include linearity (the relationships between variables are linear), additivity (the functions are additive), divisibility (variables can take any fractional values), and certainty (all coefficients in the functions are known with certainty).

Question 17

Divisibility assumption in linear programming implies
A) resources can be divided among products
B) products can be divided among customers
C) decision variables may take on integer values
D) decision variables may take on fractional values

Accepted Answer

The answer of Divisibility assumption in linear programming implies
A) resources...

Question 18

Additivity assumption in linear programming implies
A) resources can be added together to generate products
B) products can be added at any time
C) resource usage for each level of decision variable can be added up to get total usage
D) total profit for each decision variable can be added up to get total profit for the model
E) C and D

Accepted Answer

The additivity assumption in linear programming means that the total resource usage and total profit can be calculated by summing up the individual contributions of each decision variable. This implies that the effects of decision variables on resources and profit are additive, as stated in options C and D.

Question 19

Per unit contribution for a new cooker goes down by $5 \%$ as a salesman tries harder and harder to sell the cooker. For this situation
A) a linear programming model will be appropriate
B) an integer linear programming will be appropriate
C) an integer linear program may be appropriate
D) a linear program will not be appropriate
E) none of the above

Accepted Answer

The per unit contribution decreasing by $5\%$ as sales effort increases introduces a non-linear relationship between the variables (sales effort and per unit contribution), making a linear programming model inappropriate for this situation. Linear programming assumes linearity in both the objective function and the constraints, which is not the case here.

Question 20

Consider the following constraints and choose the correct answer:
Constraint A: $2 X_{1}^{2}+3 X_{2} \leq 100$ Constraint B: $2 X_{1} X_{2}+3 X_{2} \leq 1000$
A) constraint A can be used in a linear program
B) constraint $\mathrm{B}$ can be used in a linear program
C) neither can be used in a linear program
D) both may be used in a linear program
E) both may be used in an integer linear program, but not in linear program

Accepted Answer

Linear programs require all constraints to be linear. Both Constraint A and Constraint B are non-linear due to the squared term $X_{1}^{2}$ in Constraint A and the product term $X_{1}X_{2}$ in Constraint B.

Quiz 3: Linear Programming: Basic Concepts and Graphical Solutions

All linear programming problems with only two variables may be solved using graphical method.

All linear programming problems with only two variables and a maximum of 10 constraints may be solved using graphical method.

If a linear programming problem has redundant constraints, then the optimal solution without the redundant constraints will be the same as the optimal solution with the redundant constraints.

If a linear program has a feasible solution with unbounded objective function value, then it must be an unbounded problem.

If a graphically solvable linear program is unbounded, then the feasible region must be open at least in one direction.

If a graphically solvable linear program is infeasible, that implies there is no point in the graph satisfying all constraints.

If a graphically solvable linear program has multiple optimal solutions, it implies that two or more corner points are optimal.

In any graphically solvable linear program, no point other than one of the corner points of the feasible region can ever be optimal.

In any graphically solvable linear program, it is enough if we examine all the corner points of the feasible region to find an optimal solution.

In any graphically solvable linear program, if two points are feasible, then any weighted average of the two points (where weights are non-negative and add up to 1.0) will also be feasible.

If a graphically solvable linear program is unbounded, then it can always be converted to a regular bounded problem by removing a constraint.

In a graphically solvable linear program, if one of the constraints is changed from " ≤\leq≤ type" to "= type", all other things remaining the same, then the optimal solution will never change.

In a graphically solvable linear program, if one of the constraints is changed from " ≤\leq≤ type" to "= type", all other things remaining the same, the problem may become infeasible.

In a graphically solvable linear program with an optimal solution, if one of the constraints is changed from "= type" to " ≤\leq≤ type", all other things remaining the same, the problem may become infeasible.

In a graphically solvable linear program with an optimal solution, if one of the constraints is changed from "= type" to " ≥\geq≥ type", all other things remaining the same, the problem may become infeasible.

Assumptions of linear programming include

Divisibility assumption in linear programming implies

Additivity assumption in linear programming implies

Per unit contribution for a new cooker goes down by 5%5 \%5% as a salesman tries harder and harder to sell the cooker. For this situation

Consider the following constraints and choose the correct answer: Constraint A: 2X12+3X2≤1002 X_{1}^{2}+3 X_{2} \leq 1002X12​+3X2​≤100 Constraint B: 2X1X2+3X2≤10002 X_{1} X_{2}+3 X_{2} \leq 10002X1​X2​+3X2​≤1000

In a graphically solvable linear program, if one of the constraints is changed from " $\leq$ type" to "= type", all other things remaining the same, then the optimal solution will never change.

In a graphically solvable linear program, if one of the constraints is changed from " $\leq$ type" to "= type", all other things remaining the same, the problem may become infeasible.

In a graphically solvable linear program with an optimal solution, if one of the constraints is changed from "= type" to " $\leq$ type", all other things remaining the same, the problem may become infeasible.

In a graphically solvable linear program with an optimal solution, if one of the constraints is changed from "= type" to " $\geq$ type", all other things remaining the same, the problem may become infeasible.

Per unit contribution for a new cooker goes down by $5 \%$ as a salesman tries harder and harder to sell the cooker. For this situation

Consider the following constraints and choose the correct answer: Constraint A: $2 X_{1}^{2}+3 X_{2} \leq 100$ Constraint B: $2 X_{1} X_{2}+3 X_{2} \leq 1000$