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Exam 2: Linear programming: Basic Concepts

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Question 1

Multiple Choice

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What is the weekly profit when producing the optimal amounts?

A) $0
B) $400
C) $700
D) $800
E) $900

F) B) and E)
G) B) and D)

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Question 2

Multiple Choice

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Given the following 2 constraints,which solution is a feasible solution for a maximization problem?

A) (x₁,x₂ ) = (1,5)
B) (x₁,x₂ ) = (5,1)
C) (x₁,x₂ ) = (4,4)
D) (x₁,x₂ ) = (2,1)
E) (x₁,x₂ ) = (2,6)

F) A) and B)
G) D) and E)

Correct Answer

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D

Question 3

True/False

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

A linear programming problem can have multiple optimal solutions

A manager should know the following things about linear programming

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. -What is the time constraint?

Which objective function has the same slope as this one: 4x + 2y = 20

Given the following 2 constraints,which solution is a feasible solution for a minimization problem?

The equation 5x + 7y = 10 is linear

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. -Which of the following is not a feasible solution?

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

The equation 3xy = 9 is linear

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. -Which of the following is not a feasible solution?

When formulating a linear programming problem on a spreadsheet,objective cells will show the levels of activities for the decisions being made

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. -Which of the following is not a feasible solution?

Linear programming problems may have multiple goals or objectives specified

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

An objective function represents a family of parallel lines

A feasible point on the optimal objective function line is an optimal solution

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