Exam 2: Linear Programming: Basic Concepts

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A circle would be an example of a feasible region for a linear programming problem.

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Which of the following is not a component of a linear programming model?

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The equation 5x + 7y = 10 is linear.

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Which of the following constitutes a simultaneous solution to the following 2 equations? (1))3x1 + 4x2 = 10 (2))5x1 + 4x2 = 14

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One of the great strengths of spreadsheets is their flexibility for dealing with a wide variety of problems.

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The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. -What is the constraint for Colombian beans?

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An objective function represents a family of parallel lines.

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The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. -What is the objective function?

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An example of a decision variable in a linear programming problem is profit maximization.

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The parameters of a model are the numbers in the data cells of a spreadsheet.

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Figure Figure   -Where are the changing cells located? -Where are the changing cells located?

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Constraints limit the alternatives available to a decision-maker.

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Figure Figure   -Where are the data cells located? -Where are the data cells located?

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The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case. -Which of the following is not a feasible solution?

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The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. -What is the constraint for Dominican beans?

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The graphical method can handle problems that involve any number of decision variables.

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The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. -What is the sugar constraint?

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The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. -What is the weekly profit when producing the optimal amounts?

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Linear programming problems may have multiple goals or objectives specified.

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All constraints in a linear programming problem are either \le or \ge inequalities.

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