Exam 21: Supplement D Linear Programming

In a linear program, ________ represent choices the decision maker can control.

D.5 The Transportation Method Table D.1 Tanfastic, Inc., a manufacturer of swimwear, is in the process of developing a production plan for the coming spring break. The ending inventory for January is 30 units. Undertime is paid, at a rate of $5.00 per unit. Details are shown in the following POM for Windows table. -Use the information in Table D.1. Given the information in the optimal tableau, what is the inventory carrying cost, in dollars per unit per quarter?

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

Table D.3 The Harper Company is in the process of production planning for the next four quarters. The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand. Anticipation inventory is also allowed, but not backorders. Undertime is paid, at a rate of $5.00 per unit. The beginning (or current) inventory is 25 units. Details are shown in the following POM for Windows table. -Use the information in Table D.3. What is the anticipation inventory at the end of the first quarter?

Briefly describe the meaning of a shadow price. Provide an example of how a manager could use information about shadow prices to improve operations?

Use the graphical technique to find the optimal solution for this objective function and associated constraints. Maximize: Z = 8A + 5B Subject To: Constraint 1 4A + 5B ≤ 80 Constraint 2 7A + 4B ≤ 120 A, B ≥ 0 Graph the problem fully in the following space. Label the axes carefully, plot the constraints, shade the feasibility region, identify all candidate corner points, and indicate which one yields the optimal answer.

Belsky Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors. The current inventory levels and parts list for each type of fan is shown in the table. Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Scenario D.1 Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce. -Referring to Scenario D.1, what is an appropriate constraint for this scenario?

A snack food producer runs four different plants that supply product to four different regional distribution centers. The division operations manager is focused on one product, so he creates a table showing each plant's monthly capacity and each distribution center's monthly demand (both amounts in cases) for the product. The division manager supplements this table with the cost data to ship one case from each plant to each distribution center. Formulate an objective function and constraints that will solve this problem using linear programming.

Only corner points should be considered for the optimal solution to a linear programming problem.

________ is useful for allocating scarce resources among competing demands.

Table D.3 The Harper Company is in the process of production planning for the next four quarters. The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand. Anticipation inventory is also allowed, but not backorders. Undertime is paid, at a rate of $5.00 per unit. The beginning (or current) inventory is 25 units. Details are shown in the following POM for Windows table. -Use the information in Table D.3. According to the optimal production plan, what is the overtime production in the second quarter?

The ________ problem is a one-period type of aggregate planning problem, the solution of which yields optimal output quantities of a group of products or services, subject to resource capacity and market demand conditions.

A(n) ________ is the marginal improvement in the objective function value caused by relaxing a constraint by one unit.

Which of the following statements regarding linear programming is not True?

In a linear program, ________ are the limitations that restrict the permissible choices for the decision variables.

In a linear programming model, the objective function answers the question What is to be maximized?

Table D.3 The Harper Company is in the process of production planning for the next four quarters. The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand. Anticipation inventory is also allowed, but not backorders. Undertime is paid, at a rate of $5.00 per unit. The beginning (or current) inventory is 25 units. Details are shown in the following POM for Windows table. -Use the information in Table D.3. What is the total cost of the optimal production plan?

An equality constraint requires that only the points on the line described by the constraint are feasible.

The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.