Exam 22: Linear Programming

John's Locomotive Works manufactures a model locomotive.It comes in two versions-a standard (X1),and a deluxe (X2).The standard version generates $250 per locomotive for the standard version,and $350 per locomotive for the deluxe version.One constraint on John's production is labour hours.He only has 40 hours per week for assembly.The standard version requires 250 minutes each,while the deluxe requires 350 minutes.John's milling machine is also a limitation.There are only 20 hours a week available for the milling machine.The standard unit requires 60 minutes,while the deluxe requires 120.Formulate as a linear programming problem,and solve using either the graphical or corner points solution method.

Suppose that a chemical manufacturer is deciding how to mix two chemicals,A and B.A costs $5/gram and B costs $4/gram if they are ordered above the current supply level.There are currently 40 grams of A and 30 grams of B that must be used in the mix or they will expire.If a customer wants 1 kg of the mix with at least 40% A but no more than 55% A,how many grams of each chemical should be included in the mix?

In which of the following has LP been applied successfully?

A linear programming problem contains a restriction that reads "the quantity of S must be no more than one-fourth as large as T and U combined." Formulate this as a constraint ready for use in problem solving software.

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

Explain how to use the iso-profit line in a graphical maximization problem.

Sensitivity analysis of linear programming solutions can use trial and error or the analytic postoptimality method.

Suppose that a maximization LP problem has corners of (0,0), (5,0),and (0,5).How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X + 5Y?

A maximizing linear programming problem with constraints C1,C2,and C3 has been solved.The dual values associated with the problem are C1 = $2,C2 = $0.50,and C3 = $0.Which statement below is false?

Suppose that a constraint for assembly time has a shadow price of $50/hour for 15 hours in either direction and that all available assembly time is currently used (would require overtime to do more).If the salary of workers is $30 and they receive 50% extra pay for overtime what should management do?

Two methods of conducting sensitivity analysis on solved linear programming problems are ________ and ________.

A linear programming maximization problem has been solved.In the optimal solution,two resources are scarce.If an added amount could be found for only one of these resources,how would the optimal solution be changed?

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

Which of the following sets of constraints results in an unbounded maximizing problem?

Tom is a habitual shopper at garage sales.Last Saturday he stopped at one where there were several types of used building materials for sale.At the low prices being asked,Tom knew that he could resell the items in another town for a substantial gain.Four things stood in his way: he could only make one round trip to resell the goods;his pickup truck bed would hold only 1000 pounds;the pickup truck bed could hold at most 70 cubic feet of merchandise;and he had only $200 cash with him.He wants to load his truck with the mix of materials that will yield the greatest profit when he resells them. State the decision variables (give them labels).State the objective function.Formulate the constraints of this problem.Do not solve,but speculate on what might be a good solution for Tom.You must supply a set of quantities for the decision variables.Provide a sentence or two of support for your choice.

The objective of a linear programming problem is to maximize 1.50A + 1.50B,subject to 3A + 2B ≤ 600,2A + 4B ≤ 600,and 1A + 3B ≤ 420. a.Plot the constraints on the grid below b.Identify the feasible region and its corner points.Show your work. c.What is the optimal product mix for this problem?

Which of the following represents valid constraints in linear programming?

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

A shadow price (or dual value)reflects which of the following in a maximization problem?

Which of the following combinations of constraints has no feasible region?