Exam 17: Appendix: Modeling Using Linear Programming

A computer manufacturing company wants to develop a monthly plan for shipping finished products from three of its manufacturing facilities to three regional warehouses. It is thinking about using a transportation LP formulation to exactly matched capacities and requirements. Data on transportation costs (in dollars per unit), capacities, and requirements are given below: Plant Plant Plant Warehouse 1 2 Requirements X 2.41 1.63 2.09 8,000 3.18 5.62 1.74 2,000 4.12 3.16 3.09 3,000 Capacities 4,000 6,000 3,000 a. How many variables are involved in the LP formulation? b. How many constraints are there in this problem? c. What is the constraint corresponding to plant 2?

The total project cost can be minimized by minimizing crash costs.

Which of the following factors would generally NOT be part of a linear programming model for production scheduling?

Deciding on how much of each grade of gasoline to produce is an example of the linear programming model for blending applications.

A company has normal capacity for 2,500 units a month. If, x₁₁ and x₂₁ represent the production decisions variables, which of the following equations represents the occurrence of change?

ABC Products Inc. produces three products (A, B, and C) on three machines. Machines 1 and 2 are available for 40 hours a week, and Machine 3 is available for 60 hours a week. Profit contribution and standard production time in hours are given in the following table: Product A B C Profit Contribution/Unit \ 40 \ 60 \ 30 Machine \#1 (time/unit) 0.6 2.2 1.8 Machine \#2 (time/unit) 1.2 0.8 0.7 Machine \#3 (time/unit) 2.4 2.8 2.0 Only one operator per machine is required on Machines #1 and #2. Two operators are required for Machine #3. Therefore, two hours of labor must be scheduled for each hour of Machine #3's time. To restate this requirement, two operators must be scheduled for each hour of Machine #3's operation, as well as one operator for each hour of Machine #1's operation and one operator for each hour of Machine #2's operation. A total of 110 labor hours is available for assignment to the three machines during the coming week. Other production requirements are that Product A cannot account for more than 40% of the units produced and that Product C must account for at least 25% of the units produced. a. Develop the constraint for the capacity limit of Machine #1. b. Develop the constraint for the capacity limit of Machine #3. c. Develop the constraint for the labor capacity limit. d. Develop the constraint for limiting Product A to no more than 40% of the units produced. e. Develop the constraint that ensures Product C accounts for at least 25% of the units produced.

For linear programming to work for project crashing decisions, a dummy activity is needed at the beginning of the project, with a duration of zero (0) time.

What characterizes a linear function?

The transportation problem is a special type of linear programming that arises in planning the distribution of goods and services from only one supply point to several demand locations.

Explain the essence of a blending problem.

Solutions to a linear programming model that satisfy all constraints are referred to as optimal.

Any particular combination of decision variables is referred to as a(n) _____.

The precedence relationships in a network limit the activity _____.

The Northwest Flower Company owns a greenhouse, which supplies roses and carnations to florists in Oregon, Washington, and Idaho. The greenhouse can grow any combination of the two flowers. They sell the flowers in "bunches" with 25 blooms to a bunch. They have 10,000 square feet available for planting this year. Each bunch of roses takes about 4 square feet and each bunch of carnations about 5 square feet. A special fertilizer is required for the flowers: roses need 5 pounds and carnations 2 pounds. The availability of the fertilizer is limited to 5000 pounds. Sales commitments require the company to grow at least 500 bunches of roses. Profit contributions are $6 per bunch of roses and $8 per bunch of carnations. a. What is the objective function if the company wants to maximize its profits? b. What is the constraint for the square footage assuming x₁ corresponds to roses? c. What is the optimal solution point for this problem? d. What is the optimal value of the objective function?

If R_m = increase in the total production level during month 'm' compared to month m-1 and D_m = decrease in the total production level during month 'm' compared to month m-1, which of the following statements can be correct?

Discuss the concept of optimization models with examples.

Which of the following factors would generally NOT be part of a linear programming model for blending?

Differentiate between a feasible solution and an optimal solution.

If a single variable is used to represent the change in production level, only positive changes would be permitted, because of the nonnegativity requirement.

The term 'programming' is used in linear programming because these models find the best 'program' or course of action to follow.