78 A3      ! ! ! ! ! A A A ANOTE: ALL FOUR APPLIED MATH LAB TEMPLATES ARE ON THIS FILE Lab#_______ Applied Mathematics Unit (#) - 16 Teacher Information Sheet Lab Title: GOURMET HOMEMADE ROOTBEER Goals and Career Applications: Students will see a use for a linear equation. They will be able to substitute the appropriate information into the slope intercept equation. They will be able to graph this equation to find a break even point and a given profit from the sale of the homemade root beer. Students may also re-visit the use of ratios and proportions from unit 9, pg. 8-44 CORD ALGEBRA I. This lab will show how a business might use this information to project outcome of sale. Materials needed: Re-usable 12 oz. Bottles, bottle caps, 5 gal. Container, bottle capper, bio-clean/T.S.P./baking soda, BTF Iodophor iodine/bleach, root beer extract, sugar, yeast, vinyl tubing, conversion chart in Teachers Guide pg. T-51 Team Formation: 4 teams 1) sanitizers: clean/sanitize all equipment. 2) micro-biologists: determine correct proportions for all supplies. 3) production line: fill and cap bottles. 4) sales & marketing: determine reasonable selling price and create a logo for bottles Suggested Timeline: 2 to 3 class periods depending on depth of involvement. Lab Preparation: (Period 1) SANITIZERS: Bottles, 5 gal. Container, tubing must be cleaned. Use one table spoon of baking soda per gallon of water for solution ( you may use T.S. or commercial cleaning products) DO NOT use dish washing soaps. All above items and the bottle caps must be sanitized. Use one tablespoon of household bleach (use Colrox) per gallon of water or one teaspoon of BTF iodiphor iodine (this is best) per gallon. All of these items may soak until time to be used, but at least 30 minutes. This group may want to use rubber gloves; it dries the skin out. MICRO-BIOLOGISTS: The instructions and extract are for making 5 gallons of root beer. If the class is asked to make 2 gallons, this group will need to calculate proper amounts of sugar (table sugar) or the root beer will not be sweet. NOTE: as the yeast works the root beer will lose some sweetness, so an error on the side of too much sugar is better. DO NOT use corn sugar, it works too well. For yeast use ale, champagne or household baking yeast. I think champ is best. Tap water at room temperature is fine. If it is over 80F. It could kill the yeast and the root beer will be flat and bad. Follow the instruction that come with the extract. PRODUCTION LINE: This team will fill and cap each bottle. Check the caps for a good seal by turning the bottles upside and look for leaks. MARKETING AND SALES: This team will need to come up with a price that will be asked for each bottle of root beer. They must present this asking price to the class and explain how they arrived at this. They are also responsible for a logo that could be placed on the bottle. It must be tasteful. (Period 2) ALL STUDENTS: Each student is required to prepare a graph of their own. They must determine the scale etc. To do this they will need to decide which item in the lab are re-useable and which are consumable. Helpful hints: Equipment and supplies Re-useable 12 oz. bottles $ .20 Bottle caps $ .02 5 gal. Container $ 5.00 Bottle capper $14.00 Bio-clean (or baking soda) $ .01 per bottle BTF Iodophor iodine (or bleach) $ .02 per bottle Root Beer extract $ 4.95 Sugar (4 to 5 lbs. (cane not corn) $ .06 per bottle Yeast $ .50 Vinyl tubing $ 1.00 Optional Activities: Equation to use is slope intercept y=mx+b The students will need to determine which items are consumable supplies and which are reusable equipment. They should then substitute the supplies cost for m and the equipment cost for b. X is the number of bottles of root beer produced and y will be the cost for that number of bottles. Students are to graph this equation. After the price for each bottle of reet beer is determined, substitute that for m. B of course is 0. Students should then graph this eequation on the same graph. The point of intersection is the break even point. The two equations used are y=mx+b ( the cost to make the root beer) and y=mx (the income from selling the root beer). A system of equations may also be used to find the break even point and check the graph answer. This would be mx=mx+b. By solving for x the number of bottles sod to break even will be found. 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