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Exam 22: Linear Programming

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Question 1

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

A) area of optimal solutions.
B) area of feasible solutions.
C) profit maximization space.
D) region of optimality.
E) region of non-negativity.

F) A) and B)
G) A) and C)

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B

Question 2

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What is the feasible region in a linear programming problem?

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The feasible region ...

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Question 3

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What is sensitivity analysis?

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.

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

A linear programming problem has two constraints 2X + 4Y = 100 and 1X + 8Y ≤ 100,plus non-negativity constraints on X and Y.Which of the following statements about its feasible region is true?

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding,two minutes per unit for painting,and one minute for packing.Product B requires two minutes per unit for molding,four minutes for painting,and three minutes per unit for packing.There will be 600 minutes available for molding,600 minutes for painting,and 420 minutes for packing.Both products have contributions of $1.50 per unit. a.Algebraically state the objective and constraints of this problem. b.Plot the constraints on the grid below and identify the feasible region.

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.

Two methods of solving linear programming problems by hand include the corner-point method and the ________.

Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of action.

What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y,subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x,y ≥ 0.

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.

Consider the following constraints from a two-variable linear program. (1) X ≥ 1 (2) Y ≥ 1 (3) X + Y ≤ 9 If these are the only constraints,which of the following points (X,Y) cannot be the optimal solution?

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100,two of its corner points are (0,0)and (0,25).

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

If cars (C sell for $500 profit and trucks (T) sell for $300 profit which of the following represents the objective function?

A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R,S,and T." Formulate this as a constraint ready for use in problem solving software.

A stereo mail order centre has 8,000 cubic feet available for storage of its private label loudspeakers.The ZAR3 speakers cost $295 each and require 4 cubic feet of space;the ZAR2ax speakers cost $110 each and require 3 cubic feet of space;and the ZAR4 model costs $58 and requires 1 cubic foot of space.The demand for the ZAR3 is at most 20 units per month.The wholesaler has $100,000 to spend on loudspeakers this month.Each ZAR3 contributes $105,each ZAR2ax contributes $50,and each ZAR4 contributes $28.The objective is to maximize total contribution.Write out the objective and the constraints.

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?

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