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Exam 2: Linear Programming: Basic Concepts

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Question 21

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Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 2x2 = 6 (2) 6x1 + 3x2 = 12

A) (x1, x2) = (1, 1.5)
B) (x1, x2) = (0.5, 2)
C) (x1, x2) = (0, 3)
D) (x1, x2) = (2, 0)
E) (x1, x2) = (0, 0)

F) None of the above
G) A) and B)

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Question 22

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Linear programming allows a manager to find the best mix of activities to pursue and at what levels.

A) True
B) False

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Question 23

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A maximization problem can generally be characterized by having all ≥ constraints.

When solving a maximization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible.

An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B) . Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the weekly profit when producing the optimal amounts?

Since all linear programming models must contain nonnegativity constraints, Solver will automatically include them and it is not necessary to add them to a formulation.

When solving linear programming problems graphically, there are an infinite number of possible objective function lines.

The equation 3xy = 9 is linear.

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

The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the weekly profit when ordering the optimal amounts?

The line forming the boundary of what is permitted by a constraint is referred to as a parameter.

Where are the data cells located?

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. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Dominican beans?

The value of the objective function decreases as the objective function line is moved away from the origin.

If a single optimal solution exists while using the graphical method to solve a linear programming problem, it will exist at a corner point.

The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the storage space constraint?

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. The brewery's goal is to maximize profits. What is the objective function?

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

An infeasible solution violates all of the constraints of the problem.

All constraints in a linear programming problem are either ≤ or ≥ inequalities.