Exam 3: Linear Programming: Formulation and Applications

Approximations and simplifying assumptions generally are required to have a workable model.

It is the nature of the application that determines the classification of the resulting linear programming formulation.

A transportation problem with 3 factories and 4 customers will have 12 fixed-requirement constraints.

The objective cell is a special kind of output cell.

A transportation problem with 3 factories and 4 customers will have 12 shipping lanes.

Financial planning is one of the most important areas of application for cost-benefit-tradeoff problems.

For cost-benefit-tradeoff problems, minimum acceptable levels for each kind of benefit are prescribed and the objective is to achieve all these benefits with minimum cost.

A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). What is the optimal mix of jobs for the writer to accept each week?

A key assumption of linear programming is that the equation for each of the output cells, including the objective cell, can be expressed as a SUMPRODUCT (or SUM) function.

Resource-allocation problems are linear programming problems involving the allocation of limited resources to activities.

In most cases, the minimum acceptable level for a cost-benefit-tradeoff problem is set by how much money is available.

A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping\nobreakspaceCosts Customer per\nobreakspaceunit\nobreakspacePlant 1 2 3 \ 25 \ 35 \ 15 \ 20 \ 30 \ 40 \ 40 \ 35 \ 20 \ 15 \ 20 \ 25 The firm needs to satisfy all demand each day, but would like to minimize the total costs. The objective function for the firm's problem will have how many terms?

A linear programming problem may return fractional solutions for a resource allocation problem.

A benefit constraint refers to a functional constraint with a ≥ sign in a linear programming model.

A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and are then sold for a profit of $3.00 per bundle. The manager has 100 gallons of milk and 150 dozen cookies available each day. The manager has decided to stock at least 75 gallons of milk per day and demand for cookies is always 140 dozen per day. To maximize profits, how much of each product should the manager stock. The manager's problem falls within which classification?

The requirements assumption states that each source has a fixed supply of units, where the entire supply must be distributed to the destinations and that each destination has a fixed demand for units, where the entire demand must be received from the sources.

A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping\nobreakspaceCosts Customer per\nobreakspaceunit\nobreakspacePlant 1 2 3 \ 25 \ 35 \ 15 \ 20 \ 30 \ 40 \ 40 \ 35 \ 20 \ 15 \ 20 \ 25 The firm needs to satisfy all demand each day, but would like to minimize the total costs. What is the minimum daily shipping cost that the firm can achieve?

An assignment problem:

Fixed-requirement constraints in a linear programming model are functional constraints that use an equal sign.

It is the nature of the restrictions imposed on the decisions regarding the mix of activity levels that determines the classification of the resulting linear programming formulation.