Module B Linear Programming

What is the primary purpose of the mathematical technique known as linear programming (LP) in the context of operations management?

Which of the following is NOT one of the four requirements of a linear programming problem?

Glickman Electronics produces x-pods (X1) and BlueBerrys (X2). An x-pod requires 4 hours of electronic work and 2 hours of assembly. A BlueBerry requires 3 hours of electronics and 1 hour of assembly. Available time is 240 hours for electronics and 100 hours for assembly. The profit is 7 dollars per x-pod and 5 dollars per BlueBerry. What is the correct objective function for Glickman's problem?

Using the Glickman Electronics data where an x-pod (X1) takes 4 hours of electronic work and a BlueBerry (X2) takes 3 hours, with 240 total electronic hours available, what is the correct constraint for the electronics department?

What does the feasible region in a graphical LP solution represent?

According to the corner-point method of solving LP problems, an optimal solution will always lie at what location?

In the Glickman Electronics problem, the feasible region has corner points at (0, 0), (0, 80), (50, 0), and (30, 40). With an objective function of Profit = 7X1 + 5X2, what is the profit at the corner point (0, 80)?

What is the primary purpose of sensitivity analysis, or postoptimality analysis, in linear programming?

In sensitivity analysis, what does the 'shadow price' (or dual value) of a constraint represent?

A sensitivity report for the Glickman Electronics problem shows that the assembly time constraint (originally 100 hours) has a shadow price of 0.50 dollars and an allowable increase of 20 hours. If the company increases available assembly time from 100 to 110 hours, what is the new total profit?

Cohen Chemicals produces two types of photo-developing fluids. The first, a black-and-white chemical (X1), costs 2,500 dollars per ton, and the second, a color chemical (X2), costs 3,000 dollars per ton. The company must produce at least 30 tons of X1, at least 20 tons of X2, and a total of at least 60 tons of both. What is the objective function for this problem?

For the Cohen Chemicals minimization problem, the two feasible corner points are (40, 20) and (30, 30). The objective is to minimize cost = 2500X1 + 3000X2. Which corner point represents the optimal solution?

The Feed 'N Ship feedlot must create a feed mix for cattle using three grain stocks (X, Y, Z). A key nutritional requirement is for at least 80 ounces of ingredient B. The content of ingredient B per pound of grain is 2 oz for stock X, 3 oz for stock Y, and 1 oz for stock Z. Which of the following is the correct constraint for ingredient B?

For the Mexico City Bank labor scheduling problem, part-time employees must work exactly 4 hours per day. Full-time tellers work from 9 a.m. to 5 p.m. with a 1-hour lunch. Corporate policy limits part-time hours to a maximum of 50 percent of the day's total requirement. If the total teller-hours required for the day is 112, what is the constraint on part-time hours?

What is the primary characteristic of binary variables used in linear programming?

In a fixed-charge problem, Sitka Manufacturing is considering building a plant in Baytown (Y1), which has an annual fixed cost of 340,000 dollars and a capacity of 21,000 units (X1). How can the relationship between building the plant and its production capacity be modeled using a binary variable?

If you wish to model a situation where, out of three potential projects (Y1, Y2, Y3), exactly two must be selected, what would be the correct binary constraint?

How can you model the dependent selection where purchasing a catalytic converter (Y1) is only possible if the corresponding software (Y2) is also purchased?

When graphically solving a linear programming problem, what is the purpose of the iso-profit line?

In the Sitka Manufacturing fixed-charge problem, the objective is to minimize cost, which includes an annual fixed cost of 270,000 dollars if a plant is built in Lake Charles (Y2) and a variable cost of 33 dollars per unit (X2) produced there. How would this be represented in the objective function?

In the sensitivity report for Glickman Electronics, the unit profit for x-pods (X1) is 7 dollars, and the allowable increase is 3 dollars. What would happen to the optimal solution mix (30 x-pods, 40 BlueBerrys) if the profit on x-pods increased to 9 dollars?

In the sensitivity report for Glickman Electronics, the unit profit for BlueBerrys (X2) is 5 dollars, and the allowable decrease is 1.50 dollars. If the profit on BlueBerrys drops to 3 dollars per unit, what happens?

What is the general term for a numerical value that is given in a model, such as the profit per unit of a product or the hours of a resource available?

Which of the following problems is an example of a 'diet problem' application in linear programming?

In the Failsafe Electronics production-mix problem, one of the constraints is a minimum production level for product TR29 (X3) of 200 units to fulfill contracts. How is this requirement formulated as a constraint?

What is the primary drawback of forcing decision variables in a large LP program to be integer or binary?

What is a common reason for a linear programming minimization problem to be 'unbounded'?

The procedure for finding the optimal solution to a linear programming problem with more than two variables is called the simplex method. What is its basic function?

In the Mexico City Bank problem, there is a constraint for the time period 11 a.m. to noon, which requires 14 tellers. Full-time tellers (F) are on their lunch break for half of this period. Part-timers starting at 9 a.m. (P1), 10 a.m. (P2), and 11 a.m. (P3) are working. What is the correct constraint for this period?

In the Sitka Manufacturing problem, the company wishes to have a total production capacity of at least 38,000 units from the plants it decides to build. X1, X2, and X3 are the units produced at Baytown, Lake Charles, and Mobile, respectively. What is the correct formulation for this capacity constraint?

To solve the Glickman Electronics problem graphically using the iso-profit line method, an initial profit line of 210 dollars is plotted. This line is represented by the equation 210 = 7X1 + 5X2. What are the two points where this line intersects the X1 and X2 axes?

When solving the Glickman Electronics problem, the optimal solution is found at the intersection of the two constraint lines, 4X1 + 3X2 = 240 and 2X1 + 1X2 = 100. What is the optimal number of BlueBerrys (X2) to produce?

Which of the following describes the corner-point method for solving LP problems?

A sensitivity report for Glickman Electronics indicates the shadow price for electronic time is 1.50 dollars. The allowable increase is 60 hours and the allowable decrease is 40 hours from the original 240 hours. What does this information imply?

The Feed 'N Ship feedlot can obtain only 500 pounds of stock Z per month. Since there are 100 cows, this limits the amount of stock Z for each cow to no more than 5 pounds per month. How is this limitation for an individual cow (X3) formulated?

In the Mexico City Bank labor scheduling problem, the objective is to minimize the total daily manpower cost. Full-time tellers (F) cost 75 dollars per day, and part-time tellers (P1 through P5) cost 24 dollars per day. What is the objective function?

What is the general relationship for a resource constraint in a linear programming problem?

Which of the following scenarios is an example of a linear programming application in labor scheduling?

In the Glickman Electronics problem, if the company were to produce 70 x-pods (X1), why would this be an infeasible solution?

If a linear programming problem has more than two decision variables, which solution method is generally required?

What does it mean if a solution produced by an LP model has non-integer values for decision variables, such as producing 30.5 cars?

In the Failsafe Electronics problem, the objective is to maximize profit = 9X1 + 12X2 + 15X3 + 11X4. The time required for inspection for each product (X1, X2, X3, X4) is 0.5, 1.0, 0.5, and 0.5 hours respectively, with 1,200 total inspection hours available. What is the correct inspection constraint?

How do minimization problems solved graphically differ from maximization problems in terms of the feasible region's boundaries?

If you wish to model a situation where projects Y1 and Y2 must either be selected together or not selected at all, what is the correct binary constraint?

In the Cohen Chemicals problem, a constraint requires that the total production of black-and-white chemical (X1) and color chemical (X2) must be at least 60 tons. How is this formulated?

What does the term 'linearity' imply in the context of linear programming requirements?

In the Mexico City Bank scheduling problem, the number of available full-time tellers is 12. How is this fact represented as a constraint on the number of scheduled full-time tellers (F)?

For the Glickman Electronics problem, what do the nonnegativity constraints X1 >= 0 and X2 >= 0 signify?

When solving the Cohen Chemicals minimization problem, what does the iso-cost line represent?

In the Sitka Manufacturing problem, what is the purpose of using binary variables Y1, Y2, and Y3?