Exam 11: Linear Optimization Models

The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as

Two mining fields, Field A and Field B, of a coal mining company produce Lignite and Bituminous coal. The operating cost per day for Field A and Field B are $55,000 and $45,000, respectively.The recent records at the company indicate that Field A can produce 250 tons of Lignite along with 300 tons of Bituminous coal per day, whereas Field B can produce 200 tons of Lignite along with 450 tons of Bituminous coal per day. The expected demands to be met are 120,000 tons of Lignite and 170,000 tons of Bituminous coal. To minimize the operating costs of the mining fields, how many days does the company need to operate each of these fields?

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. Restrictions on the type of permissible investments would be a _________ in this case.

Problems with infeasible solutions arise in practice because

The reduced cost for a decision variable that appears in a Sensitivity Report indicates the change in the optimal objective function value that results from changing the right-hand side of the nonnegativity constraint from

A variable subtracted from the left-hand side of a greater-than-or-equal to constraint to convert the constraint into an equality is known as a(n)

Zen Inc. manufactures two types of products, the G.1 and the T.1 models. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work a 7-hour shift. On an average, to produce a G.1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T.1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T.1 models as G.1 models. The company operates five days per week and makes a net profit of $130 on the G.1 model, and $150 on the T.1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. What is the projected profit at the maximized number of units produced? ​ Let the number of G.1 product produced each week be G Let the number of T.1 product produced each week be T Maximize 130G + 150T production's labor constraint 3.5G + 4T <= 2030 assembly's labor constraint 2G + 1.5T <= 875

In problem formulation, the

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. ​ Operation Manufacturing Time (Hours) Time Available Economy tires Premium tires Hours Material Preparation 4/3 1/2 600 Tire Building 4/5 1 650 Curing 1/2 2/4 580 Final Inspection 1/5 1/3 120 Profit/Tire \ 12 \ 10 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 change in the optimal objective function value per unit increase in the right-hand side of a constraint is given by the

Zen Inc. manufactures two types of products, the G.1 and the T.1 models. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work a 7-hour shift. On an average, to produce a G.1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T.1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T.1 models as G.1 models. The company operates five days per week and makes a net profit of $130 on the G.1 model, and $150 on the T.1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. Solve Using the Excel Solver tool. ​

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 A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month.. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.

A soft drink manufacturing company has 3 factories-one in Orlando, one in Tampa, and one in Port St. Lucie-which supply 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. ​ Transportation Costs of Factories (\ ) Factories/Warehouses W1 W2 W3 Orlando 7 4 5 Tampa 7 6 4 Port St. Lucie 5 5 6 The factory in Orlando has a capacity of 14,000 units. The factory in Tampa has a capacity of 25,000 units. The factory in Port St. Lucie has a capacity of 23,000 units. The requirements of the warehouses are: Warehouse Requirement (Bottles) W1 18,000 W3 19,000 ​ 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?

The reduced cost for a decision variable that appears in a Sensitivity Report refers to the ____________ of the nonnegativity constraint for that variable.

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

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 visualization tools could help understand this problem better?

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.

The slack value for binding constraints is

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

The assumption that is necessary for a linear programming model to be appropriate and that ensures that the value of the objective function and the total resources used can be found by summing the objective function contribution and the resources used for all decision variables is known as