Exam 13: Linear Optimization

Use the case below to answer the following question(s). S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit. Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively. -Which of the following is the inequality/equality that describes the time constraint of the painting department?

A nonbinding constraint is one for which the Cell Value is equal to the right-hand side of the value of the constraint.

Use the case below to answer the following question(s). Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on. -The number of television sets shipped from the plant in Arkansas to the distribution center in San Antonio is ________.(Hint: Use Solver)

Briefly explain the difficulties experienced while using Solver to obtain optimal solutions for linear optimization models.

What is a feasible solution?

What are shadow prices? How are shadow prices useful for managers?

In linear optimization,the phrase "cannot exceed" specifies a(n)"________" inequality.

Consider the scenario given below.Use Excel solver to answer the following question(s). Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit. -Calculate the number of swivel chairs produced in a day.

In the constraints section obtained in solver reports,what is a binding constraint?

Decision variables are the unknown values that the model seeks to determine.

How does Solver create names in reports?

Use the case below to answer the following question(s). Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on. -Calculate the total number of television sets shipped from the plant in Arizona.(Hint: Use Solver)

Slack variables are always nonnegative.

S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit. Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively. -Using Solver,determine the number of hours used in the quality check department.

Use the data given below to answer the following question(s). Ball Inc.specializes in producing disinfectants.In developing a new disinfectant,company scientists have specified that the mixture must contain at least 26% hydrogen,at least 30% oxygen,and no more than 28% water.The percentages of each of these constituents in two types of ingredients that can be used to produce the disinfectant are given in the table,along with the wholesale cost per pound. Let X₁ and X₂ denote DDT and solid carbon dioxide,respectively. -The objective of the data given above is to determine the appropriate amount of ingredients to include in one pound of mix.This leads to the constraint ________.

If the Solver reports that "The Set Cell values do not converge.",the linear optimization model ________.

The ________ is the difference between the right- and left-hand sides of a constraint.

Use the case below to answer the following question(s). Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on. -Determine the equality/inequality that explains the demand constraint for the distribution center in Dallas.