MATH 312 Final: MATH 312 KSU Final Exam s99

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Correct answers without supporting work will receive no credit. (7) 1. a) when does a graph have an euler circuit? (17) b) find an euler circuit of the following graph: (17) 2. Find a minimal spanning tree for the following weighted graph: (16) 3. (p q) p . (16) 4. Show that (p q) (p q) . page 2 (16) 5. Wildcat pizza o ers four toppings: chocolate chip, licorice, butterscotch, and applesauce. 60 had exactly two toppings, 50 had exactly three toppings, 20 had all four toppings and 80 had no toppings. How many pizzas had one topping? (16) 6. Use the fact that to solve the system. Use the simplex method to maximize 2x + 3y subject page 3 to: 3x + 2y 60 x + y 50 x, y 0 (14) 8. A club has 12 women and 10 men.