In this project, students will explore the process of optimization and practice real-world modeling on Excel Solver. They will create a hypothetical business that is seeking to maximize profits. They will make a visual depicting the problem and present their findings to the class. They will present their findings to their hypothetical boss. Procedure 1. With your group members, select your problem carefully. Each person should do a rough draft of the work for the problem. At this point, you may want to make the problem your own change the name of the business, the products you are selling, or add other interesting features to the project. 2. Create a visual that fully explains your linear programming problem. Be colorful and neat. You can print out logos for your company or fake products. Be creative as possible, while maintaining professionalism. Mathematically, you must include:

List of the important facts from your problem

Meaning for the variables

Constraints

Objective function

Meaningful solution! 3. Present both problems and solutions to classboard meeting style Following are the detailed instructions to complete the project:

Prepare a Powerpoint presentation of your selected company. Each team presentation should last 20 minutes maximum. Each presentation will be followed by 2-3 minutes for questions. Your Powerpoint slides should be emailed to the instructor at least 24 hours before your scheduled presentation. Presentation will have 10 points.

Prepare a report with your answers. The report shouldnt be more than 1500 words and should contain proper figures and references.

Please remember you are the company making a presentation! You are speaking to the board members telling them what you should make and how much of it you should make in order to maximize profits or minimize costs etc. Do not speak only in mathematical terms the entire time (in terms of x and y). Explain how you came up with your equations.

Some of the potential problems are given on the next page. UD Policies & Procedures |Educational Program EP 3.9 Appendix VI 04-06-17 1. A carpentry shop makes dinner tables and coffee tables. Each week the shop must complete at least 8 dinner tables and at least 12 coffee tables to be shipped to the furniture stores. The shop can produce at most 25 dinner tables and coffee tables combined each week. If the shop sells dinner tables for $120 and coffee tables for $150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income? 2. Suppose a lumber mill can turn out 600 units of lumber and plywood each week. To meet the needs of its regular customers, the mill must produce 150 units of lumber and 225 units of plywood. If the profit for each unit of lumber is $30 and the profit for each unit of plywood is $45, how many units of each type of wood product should the mill produce to maximize profit? What is this profit? 3. Funtime Airways flies from Palau to Nauru weekly if at least 12 first class tickets and at least 16 tourist class tickets are sold. The plane cannot carry more than 30 passengers. Funtime Airways makes $26 profit for each tourist class seat sold and $24 profit for each first class seat sold. In order for Funtime Airways to maximize its profits, how many of each type of seat should they sell? What is the maximum profit? 4. Steve makes two types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 oz of varnish. It takes 2 hours to assemble an oak clock, which takes 4 oz. of varnish. Juan has 16 oz. of varnish in stock, and can work 20 hours. If he makes $3 profit on each pine clock and $4 on each oak clock, how many of each type should he make to maximize his profits? What is the maximum profit? 5. A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the profit is $500 per acre of wheat and $300 per acre of rye, how many acres of each should be planted to maximize profits? What is this profit? 6. A calculator company produces a scientific calculator and a graphing calculator. There is an expected demand of at least 60 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 100 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators must be shipped each day. If each scientific calculator is sold for a $2 profit and each graphing calculator is sold for a $5 profit, how many of each should be made daily to maximize profit? What is this maximum profit? 7. The Cruiser Bicycle Company makes two styles of bicycles: the Traveler, which sells for $200, and the Tourester, which sells $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor available for production. How many bicycles of each model should be produced to maximize revenue? 8. The B & W Leather Company wants to add handmade belts and wallets to its product line. Each belt nets the company $18 in profit, and each wallet nets $12. Both belts and wallets require cutting and sewing. Belts require 2 hours of cutting time and 6 hours of sewing time. Wallets require 3 hours of cutting time and 3 hours of sewing time. If the cutting machine is available 12 hours a week and the sewing machine is available 18 hours per week, what mix of belts and wallets will produce the most profit? What is the profit? 9. The Plexus Dance Theatre Company will appear at the University of Georgia. According to school policy, no more than 2000 general admission tickets can be sold and no more than 4000 student tickets can be sold. It costs $0.50 per ticket to advertise the dance company to the students and $1 per ticket to advertise to the general public. The dance company has an advertising budget of $3000 for this show. UD Policies & Procedures |Educational Program EP 3.9 Appendix VI 04-06-17 Find the maximum profit the company can make if it charges $4 for a student ticket and $7 for a general admission ticket. How many student and general admission tickets should they sell to maximize profit? What is this profit? 10. At a certain refinery, gasoline and fuel oil are produced. The refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. To meet the anticipated demands of the winter, at least three million gallons of fuel oil a day will need to be produced. The demand for gasoline, on the other hand, is not more than 8 million gallons a day. If the gasoline is selling for $1.90 per gallon profit and fuel oil sells for $1.50 per gallon profit, find how much of each should be produced in order to maximize profit. What is the maximum profit?