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Exam 19: Acceptance Sampling

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Question 51

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

A) x = -1, y = 1
B) x = 0, y = 4
C) x = 2, y = 1
D) x = 5, y = 1
E) x = 2, y = 0

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

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Question 52

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What is linear programming?

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Linear programming is a mathem...

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Question 53

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

What are the requirements of all linear programming problems?

__________ is a mathematical technique designed to help operations managers plan and make decisions relative to the trade-offs necessary to allocate resources.

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.

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?

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

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

A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity 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. Answer the following questions; base your work on the solution panel provided. a. What combination of A and B will maximize contribution? b. What is the maximum possible contribution? c. Are any resources not fully used up? Explain.

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

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.

What is sensitivity analysis?

Phil Bert's Nuthouse is preparing a new product, a blend of mixed nuts. The product must be at most 50 percent peanuts, must have more almonds than cashews, and must be at least 10 percent pecans. The blend will be sold in one-pound bags. Phil's goal is to mix the nuts in such a manner that all conditions are satisfied and the cost per bag is minimized. Peanuts cost $1 per pound. Cashews cost $3 per pound. Almonds cost $5 per pound and pecans cost $6 per pound. Identify the decision variables of this problem. Write out the objective and the set of constraints for the problem. Do not solve.

The graphical method of solving linear programming can handle only maximizing problems.

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

The __________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

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 labor 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.