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Exam 8: Linear Optimization Models

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Question 31

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Ethan Steel, Inc. has two factories that manufacture steel components for four different rail projects located at four different sites. 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: Shipping Details (with per-unit shipping cost): Find an alternative optimal solution for this transportation problem? Hint: Use the procedure described in section 8.7.

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First, solve the problem by minimizing t...

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Question 32

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Clever Sporting Equipment, Inc. makes two types of balls: Soccer balls and Cork balls. The making of each soccer ball and cork ball requires 3 hours and 4 hours of production time, respectively. For the next month, the total production hours of 500 are available. Also, it is given that the combined production quantity for these two balls must be at least 150 units. The objective for this linear programming model is to fulfil the given production requirements at a minimum cost for the total production. The production cost for each Soccer ball is $9 and each Cork ball is $7. Formulate and solve for the recommended production quantities.

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Let S = number of Soccer balls...

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Question 33

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The change in the optimal objective function value per unit increase in the right-hand side of a constraint is given by the _____.

Which of the following error messages is displayed in Excel Solver when attempting to solve an unbounded problem?

A(n) _____ refers to a set of points that yield a fixed value of the objective function.

The slack value for binding constraints is:

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

A controllable input for a linear programming model is known as a _____.

The shadow price of nonbinding constraints

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: 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? Hint: Use the procedure described in section 8.7.

Sunseel Industries produces two types of raw materials A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of the raw materials A and B must be at least 700 units per month. At least 400 units of the raw material B and not more than 1200 units of the raw material A must be produced per month. The processing time for the raw material A is observed to be 5 hours and for B, it is found to be 4 hours. A total of 3000 such hours are available per month. How much of each raw material should be produced in order to minimize the cost. Develop a linear program that Sunseel Industries can use to determine how many units of each raw material to produce to minimize the total cost.

Nonnegativity constraints ensure that

The study of how changes in the input parameters of a linear programming problem affect the optimal solution is known as_____.

Robin Tires, Inc. makes two types of tires, for SUV's and Hatchbacks. The firm has 500 hours of production time, 250 hours of packaging, and 150 hours available for shipping. The production time required per tire type is given in the following table: Assuming that the company is interested in maximizing the total profit contribution, find the optimal solution using Excel Solver and answer the following:a. How many hours of production time will be scheduled in each department? b. What is the slack time in each department? c. If one more hour is available for packaging, what is the change in profit? d. What is the change in profit if one more hour is available for shipping?

A scenario in which the optimal objective function contour line coincides with one of the binding constraint lines on the boundary of the feasible region leads to _____ solutions.

Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contribution per tire are given in the following table: Answer the following assuming that the company is interested in maximizing the total profit contribution. a. What is the linear programming model for this problem? b. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture? c. What is the total profit contribution Gatson can earn with the optimal production quantities?

The _____ assumption necessary for a linear programming model to be appropriate, means that the contribution to the objective function and the amount of resources used in each constraint are in accordance to the value of each decision variable.

A soft drink manufacturing company has 3 factories set up one in each of the three cities - Orland, Tampa, and Port St. Lucie and it supplies the produced soft drink bottles to 3 warehouses located in the city of Miami. The associated per-unit transportation cost between the factories and the warehouses is provided in the table below: The factory at Orlando has a capacity of 14,000 units. The factory at Tampa has a capacity of 25,000 units. The factory at Port St. Lucie has a capacity of 23,000 units. The requirements of the warehouses are: Determine how much of the company's production should be shipped from each factory to each warehouse in order to minimize the total transportation cost?

Robin Tires, Inc. makes two types of tires, for SUV's and Hatchbacks. The firm has 500 hours of production time, 250 hours of packaging, and 150 hours available for shipping. The production time required per tire type is given in the following table: Assuming that the company is interested in maximizing the total profit contribution, answer the following:a. What is the linear programming model for this problem? b. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Robin manufacture? c. What is the total profit contribution Robin can earn with the optimal production quantities?

A beverage cans manufacturer makes 3 types of soft drink cans needed for the beverage producers to fill soft drinks of three different volumes. The maximum availability of the machines' time allotted per day is 90 hours and the supply of metal is limited to 120 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans. Formulate and solve for the recommended production quantities for all the three different types cans by maximizing the profit.