Antonia goes to a nature preserve that charges $3 admission, but her mom pays, so it is free for her. She asks permission to buy a pocket knife from the trail shop so she can practice whittling, but her mom will not allow the purchase. Here is the anticipated total utility for each good: Preserve Visit Total Utility Pocket Knife Total Utility 1 42 1 60 12 75 2 100 3 105 3 110 14 123 4 115 5 135 5 105 6 141 6 85 7 144 7 60 a) Antonia's grandfather comes to town and offers to pay for as many pocket knives as she wants. How many should she buy? Explain. b) What is the marginal utility of her first visit to the preserve? c) Antonia's mom makes her return all the pocket knives, so she is back to zero. Antonia will now pay for her own preserve visits ($3). All the pocket knives are $5. Complete a table that shows the marginal utility per dollar for Antonia's potential preserve visits and pocket knife purchases. d) For her birthday, Antonia's mom gives her $20. She says that she is now mature enough to buy pocket knives, but she also must purchase admission to the preserve on her own. She buys as many preserve visits and pocket knives as she can. What is her optimal consumption bundle for visits and pocket knives? Explain. e) Does Antonia have any birthday money left?