Question 1

The fixed per-unit profit contribution coefficients of the objective function in a linear programming problem imply the following economic assumptions except:

Accepted Answer

C

Question 2

Which of the following statements concerning dual variables is (are) true?

Accepted Answer

E

Question 3

If the primal linear programming problem has two variables and four constraints (excluding the non-negativity constraints), the corresponding dual linear programming problem will have ____.

Accepted Answer

In the dual linear programming problem, the number of variables corresponds to the number of constraints in the primal problem, and the number of constraints corresponds to the number of variables in the primal problem. Therefore, if the primal has two variables and four constraints, the dual will have four variables and two constraints.

Question 4

A dual variable equal to zero in the optimal solution to a profit-maximization linear programming problem indicates that the objective function will not increase if an additional unit of the given resources is made available.

Accepted Answer

A dual variable (shadow price) of zero means that the resource is not a binding constraint, so increasing it does not affect the objective function value.

Question 5

An optimal solution of a linear programming problem always lies on the boundary of the feasible solution space.

Accepted Answer

In linear programming, the optimal solution, if it exists, is always found on the boundary of the feasible solution space due to the linear nature of both the objective function and the constraints. This is a direct consequence of the Extreme Point Theorem.

Question 6

A primal linear programming problem has multiple optimal solutions if it contains two or more variables.

Accepted Answer

The presence of two or more variables in a primal linear programming problem does not guarantee multiple optimal solutions; it depends on the specific constraints and objective function of the problem. Multiple optimal solutions occur when the objective function is parallel to a constraint boundary within the feasible region.

Question 7

Slack variables are given coefficients of ____ in the objective function.

Accepted Answer

Slack variables are introduced to convert inequalities into equalities in linear programming problems and are given coefficients of 0 in the objective function because they do not contribute to the value of the objective function; they are used to ensure feasibility of the constraints.

Question 8

In a maximization linear programming problem, the ____ variables represent the difference between the right-hand sides and left-hand sides of less than or equal to ($\le$ ) inequality constraints.

Accepted Answer

Slack variables are added to less than or equal to constraints in a linear programming problem to convert them into equalities, facilitating the use of the simplex method. They represent the unused resources or the difference between the left-hand side and right-hand side of the constraints.

Question 9

In a minimization linear programming problem, the ____ variables are subtracted from the greater than or equal to ($\ge$ ) inequality constraints in order to convert these constraints to equalities.

Accepted Answer

Surplus variables are subtracted from the greater than or equal to inequality constraints in a minimization linear programming problem to convert these constraints into equalities.

Question 10

A computer solution of large-scale linear programming problems typically employs a procedure (or variation of the procedure) known as the ____ method.

Accepted Answer

The simplex method is a widely used procedure for solving large-scale linear programming problems. It iteratively moves towards the optimal solution by traversing the edges of the feasible region defined by the constraints.

Question 11

____ variables are given coefficients of zero in the objective function of a minimization linear programming problem.

Accepted Answer

Surplus variables are given coefficients of zero in the objective function of a minimization linear programming problem.

Question 12

The Value-Pack Canning Company buys fresh fruits and vegetables from farmers, processes and cans them, and sells the output to various supermarket chains. The company is trying to determine the optimal mix of peas and green beans to process during the forthcoming period at its Fresno plant. Output is limited by the capacity of the plant and the firm's financial resources. The plant can process 4,000,000 pounds of peas or green beans (or any linear combination thereof) during the forthcoming period. The company buys peas and green beans for $.10 and $.20 per pound respectively. Purchases must be paid for at the time of delivery and the firm's current cash balance limits purchases to $600,000 during the forthcoming period. As part of long-term contracts with several supermarket chains, the firm is required to process at least 800,000 pounds of peas and 1,200,000 pounds of green beans during the period. The profit contribution of peas and green beans are $.015 and $.025 respectively. The firm desires to find the mix of peas and green beans to produce in order to maximize the total profit contribution of the plant during the forthcoming period. Let X₁ be the number of pounds of peas processed and X₂ be the number of pounds of green beans processed. (a)Formulate the problem algebraically in the linear programming framework. (b)Using graphical methods, determine the optimal mix of vegetables to process.

Accepted Answer

The answer of The Value-Pack Canning Company buys fresh fruits...

Quiz 7: Linear Programming Applications

The fixed per-unit profit contribution coefficients of the objective function in a linear programming problem imply the following economic assumptions except:

Which of the following statements concerning dual variables is (are) true?

If the primal linear programming problem has two variables and four constraints (excluding the non-negativity constraints) , the corresponding dual linear programming problem will have ____.

A dual variable equal to zero in the optimal solution to a profit-maximization linear programming problem indicates that the objective function will not increase if an additional unit of the given resources is made available.

An optimal solution of a linear programming problem always lies on the boundary of the feasible solution space.

A primal linear programming problem has multiple optimal solutions if it contains two or more variables.

Slack variables are given coefficients of ____ in the objective function.

In a maximization linear programming problem, the ____ variables represent the difference between the right-hand sides and left-hand sides of less than or equal to ( $\le$ ) inequality constraints.

In a minimization linear programming problem, the ____ variables are subtracted from the greater than or equal to ( $\ge$ ) inequality constraints in order to convert these constraints to equalities.

A computer solution of large-scale linear programming problems typically employs a procedure (or variation of the procedure) known as the ____ method.

____ variables are given coefficients of zero in the objective function of a minimization linear programming problem.

Quiz 7: Linear Programming Applications

The fixed per-unit profit contribution coefficients of the objective function in a linear programming problem imply the following economic assumptions except:

Which of the following statements concerning dual variables is (are) true?

If the primal linear programming problem has two variables and four constraints (excluding the non-negativity constraints) , the corresponding dual linear programming problem will have ____.

A dual variable equal to zero in the optimal solution to a profit-maximization linear programming problem indicates that the objective function will not increase if an additional unit of the given resources is made available.

An optimal solution of a linear programming problem always lies on the boundary of the feasible solution space.

A primal linear programming problem has multiple optimal solutions if it contains two or more variables.

Slack variables are given coefficients of ____ in the objective function.

In a maximization linear programming problem, the ____ variables represent the difference between the right-hand sides and left-hand sides of less than or equal to ( ≤\le≤ ) inequality constraints.

In a minimization linear programming problem, the ____ variables are subtracted from the greater than or equal to ( ≥\ge≥ ) inequality constraints in order to convert these constraints to equalities.

A computer solution of large-scale linear programming problems typically employs a procedure (or variation of the procedure) known as the ____ method.

____ variables are given coefficients of zero in the objective function of a minimization linear programming problem.

In a maximization linear programming problem, the ____ variables represent the difference between the right-hand sides and left-hand sides of less than or equal to ( $\le$ ) inequality constraints.

In a minimization linear programming problem, the ____ variables are subtracted from the greater than or equal to ( $\ge$ ) inequality constraints in order to convert these constraints to equalities.