MAT 150 Application Assessment 3: Maximizing Profit for a Small Business Instructions You may want to view the Hot Dog videos below, before completing this assignment: https://www.youtube.com/watch?v=6dH3KEuSXuQ https://www.youtube.com/watch?v=oph32OvyZQ8 Jane loves to bake and would like to sell her loaves of banana bread for $5 per loaf at the local community center. Given the recipe below and prices for the ingredients, answer the questions below. Jane's Recipe for Banana Bread 1c. sugar 1 tsp. baking soda 3 crushed bananas 12 cup butter, softened 12 tsp. cinnamon 12 cup chopped walnuts 2 eggs 2 cups flour 12 tsp. ground cloves Cream sugar and butter. Add eggs. Beat well. Sift in flour, baking soda, cinnamon, and cloves. Beat well. Mix in bananas and nuts. Pour into greased loaf pan. Bake for one hour at 325. Ingredient Price List (Note: these are the only sizes available at the grocery store where Jane shops)  all-purpose flour (32 oz.) $1.79 Note: Approx. 32 oz. of flour = 7.5 cup.  ground cloves (1.7 oz) $5.49 Note: 1.7oz. = 22 tsp.  bananas $0.25 each  sugar (4 lbs.) $2.89 Note: Approx. 4lbs. of sugar = 15 cups  eggs (1 doz.) $2.99  baking soda (1 lb.) $0.99 Note: Approx. 1 lb. of baking soda = 94.67 tsp.  butter (1 lb./4 sticks) $3.98 Note: one stick = 12 cup  cinnamon (2.37 oz.) $3.46 Note: 2.37 oz.= 25.8 tsp.  walnuts (8oz.) $4.49 Note: 8 oz = 1 cup Answer the following questions: 1. Using the Ingredient Price List, determine the number of each ingredient listed below that Jane will need to buy to make 70 loaves. Then calculate her total cost. (Worth up to 4 points based on correct formula usage, work provided, and your correct answer.)  all-purpose flour:  ground cloves:  bananas:  sugar:  eggs:  baking soda:  butter:  cinnamon:  walnuts: TOTAL COST: 2. If Jane makes 70 loaves of bread at $5 a loaf, what will her profit/loss be? (Worth up to 2 points based on correct formula usage, work provided, and your correct answer.) 3. When Jane makes 70 loaves of bread, what is the average cost for one loaf? (Worth up to 2 points based on correct formula usage, work provided, and your correct answer.) 4. Assuming Jane has no leftover/initial ingredients and wants to make just one loaf of banana bread, how much will it cost her? (Worth up to 4 points based on correct formula usage, work provided, and your correct answer.)  all-purpose flour:  ground cloves:  bananas:  sugar:  eggs:  baking soda:  butter:  cinnamon:  walnuts: TOTAL COST: 5. Jane obviously needs to consider raising her prices. Suppose that if Jane sells her bread for $5/loaf she can sell 300 loaves, but if she increases the price by $1/loaf she reduces her sales by 20 loaves. Determine the number of price increases that will allow Jane to maximize her profit. Let n = the number of price increases Revenue = [(# sold - (#reduction in sales) n] - [initial # sold+ (amt of increase) n] a. Find the Revenue formula for Jane's banana bread business. (Worth up to 3 points based on correct formula usage, work provided, and your correct answer.) b. Find the number of increases needed for Jane to maximize her profit. (Think vertex, n= ) (Worth up to 4 points based on correct formula usage, work provided, and your correct answer.) 6. Determine the price at which she should sell each loaf of bread. (Worth up to 2 points based on correct formula usage, work provided, and your correct answer.) 7. How many loaves will Jane need to make to maximize her revenue? (Worth up to 2 points based on correct formula usage, work provided, and your correct answer.) 8. Using the Ingredient Price List, determine the number of each ingredient listed below that Jane will need to buy to make the number of loaves found in number 7. Then calculate her total cost. (Worth up to 4 points based on correct formula usage, work provided, and your correct answer.)  all-purpose flour:  ground cloves:  bananas:  sugar:  eggs:  baking soda:  butter:  cinnamon:  walnuts: TOTAL COST: 9. Calculate the profit if Jane makes the number of loaves found in number 7 above. (Worth up to 4 points based on correct formula usage, work provided, and your correct answer.) 10. What will Jane's profit be if she maximizes her revenue? (Think: Revenue - Cost = Profit) (Worth up to 4 points based on correct formula usage, work provided, and your correct answer.)