a) There is a Cookies vending machine that sells a Rice Cracker packet for 50 cents and a Butter Cookies packet for 30 cents. Construct a simple possible Turing Machine (TM) using appropriate state transition diagram to demonstrate if enough coins have been entered for a purchase. Meaning, the TM constructed should deliver a Rice Cracker packet if coins totalling 50 cents is entered or deliver a Butter Cookies packet if coins totalling 30 cents is entered. Assume that the TM you construct accepts only 10, 20, and 50 cent coins (and no notes) and expects the buyer to give exact change. If coins more than 30 cents (to buy a Rice Cracker pack) or 50 cents (to buy a Butter Cookies pack) is given, then the TM just returns all the money. The TM should have one final state each for Rice Cracker, and Butter Cookies, and an error state if excess of coins is entered returning all the money

b) Explain by proof of contradiction using the Pumping Lemma that the language L = {a2nbnan | n > 0} is not regular.