Grandpa is very particular about his consumption of crackers and cheese. His preferences dictate he must accompany every cracker with a 10-gram slice of cheese. Having a different ratio of cheese to cracker would be a waste. However, as soon as Grandpa reaches a consumption of five crackers with cheese, his optimal cheese-to-cracker ratio doubles, going up to 20 grams of cheese per cracker. Assume cheese and crackers are perfectly divisible. a. Assume Grandpa has a budget m = $5, the price of each cracker is p = $1, and the price per gram of cheese is p = $0.10. Find the quantities demanded by Grandpa of crackers and cheese. b. Now assume m = $20, p = $1 and p2 = $0.10. Find the quantities demanded by Grandpa of crackers and cheese. c. Now assume m= $20, p = $1 and p = $0.50. Find the quantities demanded by Grandpa of crackers and cheese. d. Draw your answers to a, b and c in one single graph. e. In a different graph, draw Grandpa's income expansion path. Hint: there is a kink. f. Find the demand functions for cheese and crackers in terms of m, p and p. Hint: the demand functions must reflect the kink in the income expansion path.