MATH 1012 - 4 Linear Programming and the Transportation Problem

If a feasible region has corner points at (0, 0), (5, 0), (0, 4), and (2, 3), and the profit formula is $2.00x + $3.00y, then _______ is the maximum profit possible.

$13

Consider the feasible region identified by the inequalities. y - x ≤ 9 y - 2x ≥ 3 x ≥, y ≥ 0 Which one of the following points is a corner point? A. (2, 11) B. (0, 5) C. (6, 15)

(2, 11)

Which ordered pair satisfies the inequality 5x + 4y ≤ 200?

(20, 20)

Which ordered pair satisfies the inequality 9x + 2y ≤ 450?

(40, 10)

Find the indicator value of the cell (II, 1) in the tableau shown below.

-6 (may be wrong)

If your feasible region has corners points at (0, 0), (8, 0), (0, 12), and (4, 8), and the profit formula is 3x + 2y, the point _______ produces a mixture of products. Give your answer as two numbers separated by a comma. Do not use parentheses.

4, 8

Write the constraint inequalities for this situation: a cheeseburger requires 5 oz. of meat and 0.7 oz. of cheese while a superburger requires 7 oz. of meat and 0.6 oz. of cheese. The burger stand has 350 oz. of meat and 42 oz. of cheese available. The profit on a cheeseburger is 10 cents and the profit on a superburger is 40 cents.

5x + 7y ≤ 350, 0.7x + 0.6y ≤ 42, x ≥ 0, y ≥ 0

Apply the Northwest Corner Rule to the tableau shown below and determine the cost associated with the solution.

79

What is the total cost associated with the shipment plan shown in the tableau below?

84

What are the resource inequalities for the following situation? Producing a bookshelf requires eight boards and six screws. Producing a TV stand requires six boards and eighteen screws. Each bookshelf yields $25 profit, and each TV stand yields $20 profit. There are 120 boards and 198 screws available. Use variables x, y to denote the number of bookshelves and TV stands to be produced, respectively.

8x + 6y ≤ 25, 6x + 18y ≤ 20, x ≤ 120, y ≤ 198

If your feasible region has four corners at points (0, 0), (7, 0), (0, 4), and (5, 1), which of the following profit formula maximizes profit while only producing one product? 3x + 2y 2x + 5y x + y 2x + y All of the above.

All of the above.

In a two dimensional, two-product, linear programming problem, the set of all points that yield the same ______ is called the _____ line. (Note: The same word satisfies both blanks.)

profit x2

Where do the lines 5x + 3y = 20 and 2x - y = -14 intersect?

At the point (-2, 10)

What is the total cost before and after applying one level of the stepping stone method to the cell (II, 1) in the tableau shown below?

B. 55; 31 (may be wrong)

Which of the following are true statements? I: The simplex method and Karmarkar's algorithm can be used to solve linear programming problems, such as finding minimum cost in routing long-distance calls or finding maximum profit from selling products subject to resource constraints. II: The stepping stone method can be used to solve transportation problems, such as minimizing costs of deliveries shipped to various stores or efficiently assigning volunteers from different parts of the country to help clean up at various sites after a hurricane.

Both I and II are true.

Which of these methods for the transportation problem produces a feasible solution? Stepping Stone Method (SSM) Northwest Corner Rule (NCR) Both SSM and NCR Neither SSM nor NCR

Both SSM and NCR

A table showing costs and _______ conditions for a transportation problem is known as a tableau.

rim

The transportation problem involves minimizing the total ______ costs of meeting the required demands with supplies that are available.

shipping

Two alternatives to graphically solving linear programming problems are the ________ algorithm and Karmarkar's algorithm.

simplex

The graph of the inequality 2x + 7y ≤ 10 is a straight line. T o F

F

Using the Northwest Corner Rule, ship the larger of two rim values associated with the far top left cell. T o F

F

Producing a bookshelf requires eight boards and six screws. Producing a TV stand requires six boards and eighteen screws. Each bookshelf yields $25 profit, and each TV stand yields $20 profit. There are 120 boards and 198 screws available. Sketch the feasible region. How many bookshelves and TV stands need to be sold to realize the maximum profit? What is the maximum profit?

Nine bookshelves and eight TV stands for a maximum profit of $385

What is the profit formula for the following situation? Producing a bookshelf requires eight boards and six screws. Producing a TV stand requires six boards and eighteen screws. Each bookshelf yields $25 profit, and each TV stand yields $20 profit. There are 120 boards and 198 screws available. Use variables x, y to denote the number of bookshelves and TV stands to be produced, respectively.

P = 120x + 198y - P = 25x + 20y

Write a profit formula for this mixture problem: A company manufactures patio chairs and rockers. Each piece is made of wood, plastic, and aluminum. A chair requires one unit of wood, one unit of plastic, and two units of aluminum. A rocker requires one unit of wood, two units of plastic, and five units of aluminum. The company's profit on a chair is $7 and on a rocker is $12. The company has available 400 units of wood, 500 units of plastic, and 1450 units of aluminum.

P = 7x + 12y

The simplex algorithm always gives optimal solutions to linear programming problems. T o F

T

You are baking cookies and muffins for a bake sale. It takes 2 cups of flour and 1 cup of sugar to make a batch of cookies. It takes 3 cups of flour and 3 cups of sugar to make a batch of muffins. You only have 12 cups of flour and 9 cups of sugar. You make a profit of $1.50 on each batch of cookies and $2.00 on each batch of muffins. How would your profit change if you promised to make at least two batches of muffins?

You would make $0.50 less profit.

Your club is having a fundraiser selling flowers. You make $0.50 for each rose you sell and $0.30 for each carnation. You pay $0.75 for each rose, $0.50 for each carnation and your budget is $65.00. What changes occur in maximum profit if you can only buy 50 roses to resell?

You would make $1.50 less profit.

If the row sums and column sums in a tableau equal the rim conditions we have a ________ solution.

feasible

In a mixture problem, limited resources are combined into products so that the profit from selling those products is a _________ value.

maximum

The Stepping Stone Method (SSM) produces a feasible and _________ solution for the transportation problem.

optimal

If the optimal production policy for a linear programming problem is represented by a point on the x-axis, it means that the profit is optimized by making only one type of product. In order to maximize profit, the company needs to drop from its production line the item represented by the _____ variable.

y