Exam 22: Linear Programming

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100%.

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.

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

The feasible region in the diagram below is consistent with which one of the following constraints?

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

In terms of linear programming,the fact that the solution is infeasible implies that the "profit" can increase without limit.

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?

Sensitivity analysis helps to

________ are restrictions that limit the degree to which a manager can pursue an objective.

The Queen City Nursery manufactures bags of potting soil from compost and topsoil.Each cubic foot of compost costs 12 cents and contains 4 pounds of sand,3 pounds of clay,and 5 pounds of humus.Each cubic foot of topsoil costs 20 cents and contains 3 pounds of sand,6 pounds of clay,and 12 pounds of humus.Each bag of potting soil must contain at least 12 pounds of sand,12 pounds of clay,and 10 pounds of humus.Explain how this problem meets the conditions of a linear programming problem.Plot the constraints and identify the feasible region.Graphically or with corner points find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag.Identify the lowest cost possible.

A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 3Y ≥ 90 What is the largest quantity of X that can be made without violating any of these constraints?

Identify three examples of resources that are typically constrained in a linear programming problem.

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

The ________ is the set of all feasible combinations of the decision variables.

South Coast Papers wants to mix two lubricating oils (A and B)for its machines in order to minimize cost.It needs no less than 3,000 gallons in order to run its machines during the next month.It has a maximum oil storage capacity of 4,000 gallons.There are 2,000 gallons of Oil A and 4,000 of Oil B available.The mixed fuel must have a viscosity rating of no less than 40. When mixing fuels,the amount of oil obtained is exactly equal to the sum of the amounts put in.The viscosity rating is the weighted average of the individual viscosities,weighted in proportion to their volumes.The following is known: Oil A has a viscosity of 45 and costs 60 cents per gallon;Oil B has a viscosity of 37.5 and costs 40 cents per gallon. State the objective and the constraints of this problem.Plot all constraints and highlight the feasible region.Use your (by now,well-developed)intuition to suggest a feasible (but not necessarily optimal)solution.Be certain to show that your solution meets all constraints.

For the constraints given below,which point is in the feasible region of this maximization problem? (1)14x + 6y < 42 (2)x - y < 3 (3)x,y ≥ 0

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

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.

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R,S,and T." Formulate this as a constraint ready for use in problem solving software.

The region which satisfies all of the constraints in graphical linear programming is called the