1. Strassenfest Booth of Goodness by Glen Morgenstern

2. Business Plan/ Purpose The LMS German Club is sponsoring a booth to raise funds for club activities. We are selling authentic funnel cakes and Alpine water bottles, both in the spirit of Deutschland! Food and Drinks: Jumbo-sized funnel cake!! = $5.00 Alpine water bottle = $2.00

3. Establishing the Math Variables: x = # of jumbo-sized funnel cakes y = # of Alpine water bottles Constraints: We have $275 to purchase the ingredients for funnel cakes and bottles of water. It costs $1.25 of ingredients for one funnel cake, and $0.50 for each water bottle. Due to packaging of the water bottles, we have to sell at least 24 bottles.

4. Constraints continued We can only sell 200 funnel cakes due to time constraint. The Strassenfest Health and Safety Committee requires all vendors to sell at least one bottle of water for every 3 funnel cakes sold.

5. Income Function C = 5x + 2y

6. Inequalities y > 24 x > 0 x < 200 1.25x + 0.50y < 275 x < 3y

7. The Graph The y axis and the right edge of the graph (x < 200) are also constraints. x<200 x>0x>0

8. Algebra 1. y = 24 and x = 0 (0, 24) 2. x = 3y and y = 24 (72, 24) 3. x = 3y and 1.25x +0.5y = 275 (substitution) y = -2.5x + 550 x = 3 (-2.5x +550) x = -7.5x + 1650 8.5x = 1650

9. Algebra continued x = 194.118 194.118 = 3y y = 64.7059 (194.118, 64.7059) 4. x = 0 and 1.25x + 0.5y = 275 0.5y = 275 y = 550 1.25x + 0.5 (550) = 275 1.25x = 0 x = 0 (0, 550)

10. Algebra Continued Continued 5. x = 200 and 1.25x + 0.50y = 275 1.25 (200) + 0.50y = 275 250 + 0.50y = 275 0.50y = 25 y = 50 (200, 50) (200, 50) does not fall into the feasible region, so it is not a viable solution.

11. Work

12. My Feasible Solutions (0, 24) (72, 24) (194.118, 64.7059) (0, 550) Note: We can’t sell partial funnel cakes or water bottles, so we have to round. Also, (200, 50) is excluded because it does not fall into the feasible region.

13. Optimal Solution for Profit Cost = 1.25x + 0.5y < 275 There is more profit on funnel cake, so we need the maximum x subject to the constraint, x < 3y Algebraic solution (previous slide): (194.118, 64.7059), NEED TO ROUND TO WHOLE #’S

14. Optimal Profit Continued (195,65), cost = 1.25x + 0.5y = 276.25 violates cost constraint (194,65) satisfies x < 3y, cost = 1.25x + 0.5y = 275, ok sales = 5x + 2y = 1100; profit = $825 (194,64), cost = 1.25x + 0.5y = 274.5, ok sales = 5x + 2y = 1098; profit = $823.5 (193,66) satisfies x< 3y, cost = 1.25x = 0.5y = 274.25, ok sales= 5x+2y =1097; profit = $822.75 Optimum is (194,65) (funnel cakes, H2O) Profit = $825