Exam 21: Supplement D Linear Programming

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. The plant has no limits on the number of units produced by overtime or subcontractors and adopts a chase plan strategy for the six-month planning period. What is the cost for month 6 of their chase plan?

________ is an assumption that the decision variables must be either positive or zero.

Consider a corner point to a linear programming problem, which lies at the intersection of the following two constraints: 6X₁ + 15X₂ ≤ 390 2X₁ + X₂ ≤ 50 Which of the following statements about the corner point is True?

Decision variables are represented in both the objective function and the constraints while formulating a linear program.

In a linear programming model formulation, what is the meaning of a slack or surplus variable?

Parameters that are quantified without doubt meet the linear programming assumption of ________.

________ occurs in a linear programming problem when the number of nonzero variables in the optimal solution is fewer than the number of constraints.

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 inventory carrying cost, in dollars per unit per quarter?

What are the limitations of the graphical method of linear programming?

For the line that has the equation 4X₁ + 8X₂ = 88, an axis intercept is:

For an "equal" constraint, only points ________ are feasible solutions.

A manager is interested in deciding production quantities for products A, B, and C. He has an inventory of 20 tons each of raw materials 1, 2, 3, and 4 that are used in the production of products A, B, and C. He can further assume that he can sell all of what he makes. Which of the following statements is correct?

A(n) ________ limits the ability to improve the objective function.

An = (equal to) constraint is often used for certain mandatory relationships.

A manufacturer builds finished items A, B, and C from five different components. They currently have several finished units, a number of items that are partially complete, and many components that have just been delivered from their suppliers. The finished items, incomplete items and raw components can all be assigned some monetary value even though the manufacturer typically does not sell anything except finished items. The manufacturer needs to raise capital quickly so they formulate a linear program to help them decide on the most profitable way ahead. Their linear programming expert forgets to restrict their decision variables to non-negative values and is surprised when the computer output tells them that finished item A and C should be negative. If the company always follows the advice of their linear programming analysis, what should they do and why?

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 chase plan for the planning period, what will the regular output be for month 1?

A binding constraint has slack but does not have surplus.

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, which of the following statements is best?

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. Milo Belsky decided to arrive at an optimal production quantity using linear programming. His initial solution was to produce 50 Fan As and 21.4 Fan Cs for a profit of $1,542.86. Determine what his inventory would be. Charlie Belsky made an important change to the model and ran the linear programming software again, His solution was to produce 50 Fan As, -150 Fan Bs, and 150 Fan Cs for a profit of $1,650 units. What change did he make to the model and what would the ending inventory be if they were to produce according to this plan? What are the practical implications of this solution?

________ is the amount by which the left-hand side exceeds the right-hand side in a linear programming model.