Ethan Steel, Inc. has two factories that manufacture steel components for four different rail projects. The demand for the steel components for the four projects, Project A, Project B, Project C, and Project D, are 3220, 3675, 4125, and 2975, respectively. The shipping details are as below. Production Details: \[\begin{array} { l c } \text { Factory } & \begin{array} { c } \text { Maximum } \\ \text { Capacity } \end{array} \\ \hline 1 & 6500 \\ 2 & 8500 \end{array}\] Shipping Details (with per-unit shipping cost): \[\begin{array} { l c c c c } & { \text { Project } } \\ \hline \text { Factory } & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline 1 & \$ 7 & \$ 7 & \$ 8 & \$ 4 \\ 2 & \$ 6 & \$ 5 & \$ 7 & \$ 3 \end{array}\] What is the optimal (cost minimizing) distribution plan for this transportation problem?

Let x 11 : number of steel components shippe

A) quantities to be maximized in a linear programming model. B) quantities to be minimized in a linear programming model. C) restrictions that limit the settings of the decision variables. D) input variables that can be controlled during optimization. A) quantities to be maximized in a linear programming model. B) quantities to be minimized in a linear programming model. C) restrictions that limit the settings of the decision variables. D) input variables that can be controlled during optimization.

Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors in the city located at A, B, and C locations. The plants' daily capacities are 4500, 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below. \[\begin{array}{l} \begin{array} { l c c c } &\text { Distributor }\\ \hline \text { Plant } & \text { A } & \text { B } & \text { C } \\ \hline \text { P1 } & 0.8 & 0.5 & 1 \\ \text { P2 } & 0.7 & 0.65 & 0.8 \\ \text { P3 } & 0.5 & 0.45 & 0.7 \end{array} \end{array}\] Because of a failure of expected supply earlier, the distributors this time have decided to charge a penalty of $0.45, $0.55, and $0.5 per gallon, respectively for the locations A, B, and C to avoid any further delays. Find an alternative optimal solution for this transportation problem?

First, solve the problem by minimizing t

Jackson just obtained $240,000 by selling mutual funds and is now looking for other investment opportunities for these funds. His financial consultant recommends that all new investments be made in the stocks of industries such as Agriculture, Healthcare, Banking, Manufacturing, and Real Estate. The projected annual rates of returns for the investments are as follows: \[\begin{array} { | l | c | } { \text { Expected Annual Returns of the Stocks } } \\ \hline \text { Stocks } & \text { Return (\%) } \\ \hline \text { Agriculture } & 11 \\ \hline \text { Health Care } & 6.50 \\ \hline \text { Banking } & 9 \\ \hline \text { Manufacturing } & 12 \\ \hline \text { Real Estate } & 8.50 \\ \hline \end{array}\] His consultant has set constraints on the investments based on the calculated risks involved with the industries: 1) Neither Agriculture nor Manufacturing should receive more than $100,000. 2) Neither Healthcare nor Banking should receive more than $50,000. 3) The amount invested in Manufacturing should not be more than 45 percent of the sum of the investment in Banking and Healthcare sectors. 4) The amount invested in Real Estate should be at least 20 percent of the sum of the investment in Banking and Healthcare sectors. Develop portfolio recommendations-investments and amounts-for investing the available $240,000.

Let X 1 = amount invested in Agriculture

Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors located in the city at three different locations A, B, and C. The plants' daily capacities are 4500, 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below. \[\begin{array}{l} \begin{array} { l c c c } &\text { Distributor }\\ \hline \text { Plant } & \text { A } & \text { B } & \text { C } \\ \hline \text { P1 } & 0.8 & 0.5 & 1 \\ \text { P2 } & 0.7 & 0.65 & 0.8 \\ \text { P3 } & 0.5 & 0.45 & 0.7 \end{array} \end{array}\] Because of a failure of expected supply earlier, the distributors - A, B, and C this time have decided to charge a penalty of $0.45, $0.55, and $0.5 per gallon, respectively, to avoid any further delays. Now, determine the optimum supply of gasoline to the distributors, in order to minimize the total transportation cost as well as the charges payable as penalty.

Let x 11 : number of gallons of gasoline sup

Exam 11: Linear Optimization Models

Rob is a financial manager with Sharez, an investment advisory company. He must select specific investments-for example, stocks and bonds-from a variety of investment alternatives. Which of the following statements is most likely to be the objective function in this scenario?

(Multiple Choice)

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Question 41

____________ is the situation in which no solution to the linear programming problem satisfies all the constraints.

(Multiple Choice)

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Question 42

In linear programming models of real problems, the occurrence of an unbounded solution means that the

(Multiple Choice)

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Question 43

Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit?

(Multiple Choice)

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Question 44

The ___________ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint.

(Multiple Choice)

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Question 45

Hire-a-Car System rents three types of cars at two different locations. The profit contribution made per day for each car type at each location is listed below. Car Type Location Economy Mid-size Luxury A \ 25 \ 40 \ 10 B \ 30 \ 35 \ 45 The management forecasts the demand per day by car type as follows: 125 rentals for Economy cars, 55 rentals for Mid-size cars, and 40 rentals for Luxury cars. The vehicle capacity of each location is 100 cars in location A and 120 cars in location B. Develop a linear programming model to maximize profit and determine how many reservations each location should accept for each type of car. Is the demand for any car type not satisfied? Explain.

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Question 46

A canned food manufacturer has its manufacturing plants in three locations across a state. Their product has to be transported to three central distribution centers, which in turn disperse the goods to seventy-two stores across the state. Which of the following is most likely to be the objective function in this scenario?

(Multiple Choice)

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Question 47

_____________ or modeling, is the process of translating a verbal statement of a problem into a mathematical statement.

(Multiple Choice)

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Question 48

A beverage can manufacturer makes 3 sizes of soft drink cans-Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 90 production hours per day, and the daily supply of metal, no more than 120 kg per day.The following table provides the details of the input needed to manufacture one batch of 100 cans for each size cans Large Medium Small Maximum Metal (kg)/batch 9 6 5 120 Machines' Time (hr)/batch 4.4 4.2 4 90 Profithatch \ 50 \ 45 \ 42 Develop a linear programming model to maximize profit and determine how many batches of each can size should be produced.

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Question 49

Ethan Steel, Inc. has two factories that manufacture steel components for four different rail projects. The demand for the steel components for the four projects, Project A, Project B, Project C, and Project D, are 3220, 3675, 4125, and 2975, respectively. The shipping details are as below. Production Details: Factory Maximum Capacity 1 6500 2 8500 Shipping Details (with per-unit shipping cost): Project Factory A B C D 1 \ 7 \ 7 \ 8 \ 4 2 \ 6 \ 5 \ 7 \ 3 What is the optimal (cost minimizing) distribution plan for this transportation problem?

(Essay)

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Question 50

The points where constraints intersect on the boundary of the feasible region are termed as the

(Multiple Choice)

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Question 51

A company has three treatments that it can apply three different types of clothes namely denims, linens and suiting yielding the profit $4, $5, and $8 per bolt respectively. One bolt of denims requires 2 hours in Treatment 1, 3 hours in Treatment 2 and 4 hours in Treatment 3. Similarly one bolt of linens requires 3 hours in Treatment 1, 2 hours in Treatment 2 and 4 hours in Treatment 3 while one bolt suiting requires 2 hours in Treatment 1, 3 hours in Treatment 2 and 4 hours in Treatment 3. In a week, total run time of each department is 80 hours, 90 hours, and 65 hours for Treatment 1, Treatment 2 and Treatment 3 respectively. Formulation Let D₁ number of bolts of denims with Treatment 1 D₂ number of bolts of denims with Treatment 2 D₃ number of bolts of denims with Treatment 3 . . . S₃ number of bolts of Suiting with Treatment 3 Max $4(DW + DI + DP) + $5(LW + LI + LP) +$8(SW + SI + SP) s.t. 2D₁ + 3L₁ + 3S₁ ≤ 80 3D₂ + 2L₂ + 3S₂ ≤ 90 4D₃ + 4L₃ + 3S₃ ≤ 65 D₁, D₂, D₃, …, S₃ ≥ 0

(Essay)

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Question 52

When formulating a constraint, care must be taken to ensure that

(Multiple Choice)

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Question 53

Constraints are

(Multiple Choice)

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Question 54

Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors in the city located at A, B, and C locations. The plants' daily capacities are 4500, 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below. Distributor Plant A B C P1 0.8 0.5 1 P2 0.7 0.65 0.8 P3 0.5 0.45 0.7 Because of a failure of expected supply earlier, the distributors this time have decided to charge a penalty of $0.45, $0.55, and $0.5 per gallon, respectively for the locations A, B, and C to avoid any further delays. Find an alternative optimal solution for this transportation problem?

(Essay)

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Question 55

Jackson just obtained $240,000 by selling mutual funds and is now looking for other investment opportunities for these funds. His financial consultant recommends that all new investments be made in the stocks of industries such as Agriculture, Healthcare, Banking, Manufacturing, and Real Estate. The projected annual rates of returns for the investments are as follows: Expected Annual Returns of the Stocks Stocks Return (\%) Agriculture 11 Health Care 6.50 Banking 9 Manufacturing 12 Real Estate 8.50 His consultant has set constraints on the investments based on the calculated risks involved with the industries: 1) Neither Agriculture nor Manufacturing should receive more than $100,000. 2) Neither Healthcare nor Banking should receive more than $50,000. 3) The amount invested in Manufacturing should not be more than 45 percent of the sum of the investment in Banking and Healthcare sectors. 4) The amount invested in Real Estate should be at least 20 percent of the sum of the investment in Banking and Healthcare sectors. Develop portfolio recommendations-investments and amounts-for investing the available $240,000.

(Essay)

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Question 56

Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors located in the city at three different locations A, B, and C. The plants' daily capacities are 4500, 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below. Distributor Plant A B C P1 0.8 0.5 1 P2 0.7 0.65 0.8 P3 0.5 0.45 0.7 Because of a failure of expected supply earlier, the distributors - A, B, and C this time have decided to charge a penalty of $0.45, $0.55, and $0.5 per gallon, respectively, to avoid any further delays. Now, determine the optimum supply of gasoline to the distributors, in order to minimize the total transportation cost as well as the charges payable as penalty.

(Essay)

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Question 57

A mathematical function in which each variable appears in a separate term and is raised to the first power is known as a

(Multiple Choice)

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Question 58

Showing 41 - 58 of 58

Rob is a financial manager with Sharez, an investment advisory company. He must select specific investments-for example, stocks and bonds-from a variety of investment alternatives. Which of the following statements is most likely to be the objective function in this scenario?

____________ is the situation in which no solution to the linear programming problem satisfies all the constraints.

In linear programming models of real problems, the occurrence of an unbounded solution means that the

Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit?

The ___________ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint.

_____________ or modeling, is the process of translating a verbal statement of a problem into a mathematical statement.

The points where constraints intersect on the boundary of the feasible region are termed as the

When formulating a constraint, care must be taken to ensure that

Constraints are

A mathematical function in which each variable appears in a separate term and is raised to the first power is known as a

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Probability: an Introduction to Modeling Uncertainty

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

Exam 11: Linear Optimization Models

Rob is a financial manager with Sharez, an investment advisory company. He must select specific investments-for example, stocks and bonds-from a variety of investment alternatives. Which of the following statements is most likely to be the objective function in this scenario?

____________ is the situation in which no solution to the linear programming problem satisfies all the constraints.

In linear programming models of real problems, the occurrence of an unbounded solution means that the

Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit? ​

The ___________ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint.

_____________ or modeling, is the process of translating a verbal statement of a problem into a mathematical statement.

The points where constraints intersect on the boundary of the feasible region are termed as the

When formulating a constraint, care must be taken to ensure that

Constraints are

A mathematical function in which each variable appears in a separate term and is raised to the first power is known as a

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Probability: an Introduction to Modeling Uncertainty

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit?