Exam 21: Supplement D Linear Programming

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 overtime cost in dollars per unit?

A producer has three products, A, B, and C, which are composed from many of the same raw materials and subassemblies by the same skilled workforce. Each unit of product A uses 15 units of raw material X, a single purge system subassembly, a case, a power cord, three labor hours in the assembly department, and one labor hour in the finishing department. Each unit of product B uses 10 units of raw material X, five units of raw material Y, two purge system subassemblies, a case, a power cord, five labor hours in the assembly department, and 90 minutes in the finishing department. Each unit of product C uses five units of raw material X, 25 units of raw material Y, two purge system subassemblies, a case, a power cord, seven labor hours in the assembly department, and three labor hours in the finishing department. Labor between the assembly and finishing departments is not transferable, but workers within each department work on any of the three products. There are three full-time (40 hours/week) workers in the assembly department and one full-time and one half-time (20 hours/week) worker in the finishing department. At the start of this week, the company has 300 units of raw material X, 400 units of raw material Y, 60 purge system subassemblies, 40 cases, and 50 power cords in inventory. No additional deliveries of raw materials are expected this week. There is a $90 profit on product A, a $120 profit on product B, and a $150 profit on product C. The operations manager doesn't have any firm orders, but would like to make at least five of each product so he can have the products on the shelf in case a customer wanders in off the street. Formulate the objective function and all constraints, and clearly identify each constraint by the name of the resource or condition it represents.

A very confused manager is reading a two-page report given to him by his student intern. "She told me that she had my problem solved, gave me this, and then said she was off to her production management course," he whined. "I gave her my best estimates of my on-hand inventories and requirements to produce, but what if my numbers are slightly off? I recognize the names of our four models W, X, Y, and Z, but that's about it. Can you figure out what I'm supposed to do and why?" You take the report from his hands and note that it is the answer report and the sensitivity report from Excel's solver routine. Explain each of the highlighted cells in layman's terms and tell the manager what they mean in relation to his problem.

NYNEX must schedule round-the-clock coverage for its telephone operators. To keep the number of different shifts down to a manageable level, it has only four different shifts. Operators work eight-hour shifts and can begin work at either midnight, 8 a.m., noon, or 4 p.m. Operators are needed according to the following demand pattern, given in four-hour time blocks. Formulate this scheduling decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Table D.2 Bahouth Enterprises produces a variety of hookahs for clients around the globe. Their small plant has a highly flexible workforce that can switch between products seamlessly. They forecast using a six-month planning period and have a demand forecast as shown in the table. The per-unit costs for each output option the sales and operations planner has at his disposal are indicated in the table. Regular output costs $40 per unit, overtime production is $60 per unit, and subcontracting is $70 per unit. Holding inventory from one month to the next costs $2 per unit per month and a backlog costs $5 per unit per month. Regular plant capacity is 300 units per month. -Use the information in Table D.2. If the plant has no limits on the number of units produced by overtime or subcontractors, what is the lowest-cost chase plan that is possible for the six-month period?

In linear programming, a(n) ________ is a point that lies at the intersection of two (or possibly more) constraint lines on the boundary of the feasible region.

You are faced with a linear programming objective function of: Max P = $20X + $30Y And constraints of: 3X + 4Y = 24 (Constraint A) 5X - Y = 18 (Constraint B) You discover that the shadow price for Constraint A is 7.5 and the shadow price for Constraint B is 0. Which of these statements is True?

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 total ending inventory in the second quarter? Assume that the plan that uses the least amount of subcontracting is used.

What is degeneracy in the context of linear programming? Why is degeneracy a concern?

A manager is interested in using linear programming to analyze production for the ensuing week. She knows that it will take exactly 1.5 hours to run a batch of product A and that this batch will consume two tons of sugar. This is an example of the linear programming assumption of:

When plotting constraints, it is best to ignore the inequality aspect of the equation.

The simplex method is an interactive algebraic procedure for solving linear programming problems.

The interval over which the right-hand-side parameter of a constraint can vary while its shadow price remains valid is the ________.

Which of the following statements regarding linear programming is best?

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. Given the information in the optimal tableau, what is the subcontracting cost, in dollars per unit?

Table D.2 Bahouth Enterprises produces a variety of hookahs for clients around the globe. Their small plant has a highly flexible workforce that can switch between products seamlessly. They forecast using a six-month planning period and have a demand forecast as shown in the table. The per-unit costs for each output option the sales and operations planner has at his disposal are indicated in the table. Regular output costs $40 per unit, overtime production is $60 per unit, and subcontracting is $70 per unit. Holding inventory from one month to the next costs $2 per unit per month and a backlog costs $5 per unit per month. Regular plant capacity is 300 units per month. -Use the information in Table D.2. If the planner decides to adopt a level plan for the planning period, what will the total output be for month 3?

What are the assumptions of linear programming? Provide examples of each.

The simplex method deals exclusively with corner points

The objective function Maximize Z = 3x² ⁺ 4y is appropriate for linear programming.

The graphical method is a practical method for solving product mix problems of any size, provided the decision maker has sufficient quantities of graph paper.