Linear Programming Project Rubric Algebra 2 Names:
Directions: work in the group that you have been given. You will complete a linear programming problem given to you. You will create a poster board to present your answers and findings. Poster board should include the following:
1. The problem.
2. The constraints.
3. The graph of the feasible region properly shaded and the vertices labeled.
4. The objective function.
5. A chart analyzing the vertices.
6. A paragraph explaining your findings.
Rubric
Creativity and Neatness / Points Awarded with comments5 - The work is presented in a neat, clear, organized fashion that is easy to read. Students took time to personalize the project and make it their own. Care was taken so that the project looked nice, was colorful, and pleasing to the eye.
4 - The work is presented in a neat, clear, and organized fashion that is mostly easy to read. Some effort was made to personalize the project. Some effort was made to make the project look nice, colorful, and dynamic.
3 - The work is presented in a neat and organized fashion that is usually easy to read. Either effort was made to personalize the project or make it nice, colorful, and dynamic, but not both.
2 - The work is presented in an organized fashion but may be hard to read at times. Little effort made to personalize the project and it is not colorful or dynamic
1 - The work appears sloppy and unorganized. It is hard to know what information goes together. No attempt was made to personalize the project or make it colorful and dynamic.
Constraints
5 – 1)All constraints are written correctly. 2)Variables are clearly defined. 3)Constraints are organized, easy to read and clearly labeled.
4 – 1 mistake made in one of the areas above
3 – At least 2 mistakes made in the areas above
2 – At least 4 mistakes made in the areas above
1 – At least 5 mistakes made in the areas above
0 – Student did not attempt to write constraints/objective function or did not include them in the project.
Graph
5 – No graphing errors: 1) Graphed correctly 2)vertices clearly labeled 3)Scale is clearly shown on x/y axis. 4)Both x/y axis are labeled appropriately.
4 – Student made at least 1 graphing error either in the graph or in the vertices/labels.
3 – Student made at least 2 graphing errors either in the graph or in the vertices/labels.
2 – Student made at least 4 graphing errors either in the graph or in the vertices/labels.
1 – Student made at least 5 either in the graph or in the vertices/labels.
0 – Student did not attempt to graph the constraints
Conclusion – Vertices Evaluated, objective function written
5 – 1) Student listed ALL the vertices. 2)Student correctly wrote the objective function and labeled it. 3 Student correctly evaluated all the vertices neatly. 4)Student answered the problem correctly and put the answer in a correct sentence.
4 – 1 mistake made in one of the areas above
3 – At least 2 mistakes made in the areas above
2 – At least 4 mistakes made in the areas above
1 – At least 5 mistakes made in the areas above
0 – Student did not write the objective function or did not evaluate the vertices in the objective function.
Total Score (out of 40 points) / /40
1. Mary works selling cards over the telephone. She sells two types of cards, birthday cards and holiday cards. Mary makes $2.00 for each box of birthday cards she sells, and she makes $2.50 for each box of holiday cards she sells. She can work no more than 10 hours per week. It takes her an average of 15 minutes to sell one box of birthday cards and an average of 20 minutes to sell one box of holiday cards. If she can sell no more than 35 boxes of cards in total, how many boxes of each type should she sell to make the most money? (Hint: remember that an hour contains 60 minutes!)
2. Your factory makes fruit filled breakfast bars and granola bars. For each case of breakfast bars, you make a $40 profit. For each case of granola bars, you make a $55 profit. It takes 2 machine hours to make a case of breakfast bars and 5 hours of labor. It takes 6 machine hours and 4 labor hours to make s case of granola bars. You have a maximum of 150 machine hours and 160 labor hours available. How many cases of each product should you produce in order to maximize profit?
3. An oil refinery has a maximum production of 2,000 barrels of oil per day. It produces two types of petroleum products; gasoline and heating oil. The government requires that the refinery produce at least 300 barrels of heating oil per day. If the profit is $3.00 per barrel of gasoline and $2 a barrel for heating oil, how much of each petroleum product should the oil refinery produce per day to maximize profit? What is the maximum profit per day?
4. A Virginia Beach farmer has 480 acres of land on which to grow either corn or soybeans. He figures he has 800 hours of labor available during the crucial summer season. The farmer can expect a profit of $40 per acre on corn and $30 per acre on soybeans. He knows that corn requires 2 hours per acre to raise, and soybeans require 1 hour per acre to raise. How many acres of each should he plant to maximize profit? What is his maximum profit?
5. Brad owns a news stand that has room for 100 newspapers per day. In his town, there are two papers, The Journal and The Globe. Every day, Brad sells 20 Journals and 25 Globes to customers with subscriptions. If Brad makes $0.05 for every Journal sold and $0.10 for each Globe sold, how many Journals and how many Globes should he put on his stand to make the most money?
6. Your club plans to raise money by selling two sizes of fruit baskets. The Plan is to buy small baskets for $10 and sell them for $16, then buy large baskets for $15 and sell them for $25. The club president estimates that you will not sell more than 100 baskets. Your club can afford to spend up to $1,200 to but baskets. Find the number of small and large fruit baskets you should buy in order to maximize profit.