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Exam 2: Linear Programming: Basic Concepts

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Question 1

Multiple Choice

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Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 6x + 10y subject to $2 x + 4 y \geq 12$ $\begin{array} { l } 5 x + 2 y \geq 10 \\and~~~~x \geq 0 , y \geq 0 .\end{array}$

A) (x, y) = (0, 0)
B) (x, y) = (0, 3)
C) (x, y) = (0, 5)
D) (x, y) = (1, 2.5)
E) (x, y) = (6, 0)

F) C) and E)
G) B) and C)

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D

Question 2

Multiple Choice

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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. Which of the following is not a feasible solution?

A) (D, T) = (0, 0)
B) (D, T) = (0, 250)
C) (D, T) = (150, 0)
D) (D, T) = (90, 100)
E) (D, T) = (0, 200)

F) C) and E)
G) A) and E)

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Question 3

Multiple Choice

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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

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 time constraint?

For the products A, B, C, and D, which of the following could be a linear programming objective function?

In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as:

What is the time constraint?

The feasible region only contains points that satisfy all constraints.

Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 12x + 4y $\begin{aligned}\text { subject to } 2 x + 4 y & \geq 12 \\5 x + 2 y & \geq 10 \\\text { and } \quad x \geq 0 , y & \geq 0 .\end{aligned}$

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

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

Using Excel's Solver add-in, find the optimal solution for the following problem? Maximize P = 8x + 3y subject to $2 x + 4 y \leq 20$ $6 x + 3 y \leq 18$ $and\quad x \geq 0 , y \geq 0$

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

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 objective function?

Where are the changing cells located?

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

A local bagel shop produces bagels (B) and croissants (C) . Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the sugar constraint?

A manager should know the following things about linear programming.

Given the following 2 constraints, which solution is a feasible solution for a maximization problem? (1) 14x1 + 6x2 ≤ 42 (2) x1 − x2 ≤ 3

Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 3x + 15y subject to $2 x + 4 y \geq 12$ $~~~~~~~~~~~~~~5 x + 2 y \geq 10$ And x ? 0, y ? 0.