Jane's grandmother (A) and grandmother (B) both use onions and garlic in all their meals. However, the usage patterns are slightly different. Namely, A always uses two kilograms of onion with one garlic (two kilograms of onion and one garlic are the perfect complement); B, on the other hand, uses two pounds of onion or one garlic (two pounds of onion and one garlic is the perfect substitute). Let A and B, who go to the same market for their shopping, allocate their budgets for onion and garlic respectively IA = 40TL and IB = 32TL. The price of a kilo of onion is 4 TL and garlic is 12 TL. However, if the market has made a special campaign for that day and the customer buys more than two garlic, they can buy the others (from the third) for 4 TL.

a) Write the utility functions of A and B.

b)Write the budget constraint equation for A and B.

c) What will be the optimal choices of A and B? Describe using two separate graphs.

D) Explain why you cannot use the Lagrange method when finding the optimal choices of A and B.