ete It of Maximize the Candy Growing up Dr. Ecoo had a sweet tooth and liked to go candy store after school to buy chocolate bars for 8 cents each and pieces of candy for 3 cents each. The young Dr. Ecco loved candy and chocolate so much, that he wanted to spend all of his money on those two treats on every trip to the store. Dr. Ecoo never wanted to have any change lef't overI he wanted to pay in exact change on every trip to the store and use every possible cent to get as much candy as possible. P\": "Dr. Eoco can go to the store with exactly in cents and buy some combination of 8cent chocolate bars and S-cent candies without having any change left over." Show P\" is true for n 2 14 using strong induction. For our base case, we will show that our smallest valueis] of P\" isfare true. We may need more than 1 base case. but we will definitely have to show that Sis true The feedback for this part should read "The variables found in your answer were: [PM i\" In orderto determine if our base case step is complete, or if we will need to show any more base cases, we will first take a look at our inductive step. For our inductive step, we know that we are working with 2 prices, a chocolate bar price of D cents, and a candy price of C] Of these two prices, since the smaller price is 3 cents, it might be helpful to see what we can The feedback for this part should read "The variables found in your answer were: [Pn+3 1\" When we consider rt + 3 cents, we can break it up into 3 cents and n. cents. We know that 3 cents {No answer given} : be made from a combination of 8 cents and 3 cents. That is, if Dr. Ecco had 3 cents on any given day, Dr. Ecco would simply buy 1 piece of candy. So, we will consider if we can make :1 cents from a combination of 8 cents and 3 cents. Using strong inductionI we can assume that n cents can be made from a combination of 8 cents and 3 cents. That is, we will assumethat n = 3x + By where x, y E Z So our inductive step will show that {No answer given) => P+3 If we show that the base case P14 is true and the inductive step Pn => PM\" is true it would mean that: The feedback for this part should read "The variables found in your answer were: an- J\" Since there [No answer given] missing cases, we {No answer given] include more base cases. E: Show that S l:] and D are true. The feedback for these three parts should read "The variables found in your answer were: I P T" IAIh-l'n P 1": m1 inflamm