Tintin is a young Belgian reporter and an adventurer. He is currently in Shanghai, China, working on his case, "The Blue Lotus", with his wire fox terrier, Snowy. In the midst of his busy schedule, Tintin needs to figure out what to eat for lunch. His aim is to maximize his utility/satisfaction level from consuming the meal.

Tintin has two food choices available to him: one of China's famous noodles dish, Dandanmian, and some pearl meatballs, a delicious dish from central China.

Tintin is a young and busy reporter with a healthy appetite. He needs to find out the optimal number of noodles servings and meatballs servings that will maximize his satisfaction from lunch.

Let one small bowl (i.e., one serving) of dandanmian be denoted byX_1,and the price of one serving to be3Chinese yuan.

Let one serving of pearl meatballs be denoted byX₂and the price of one serving to be4Chinese yuan.

Tintin has24 yuanavailable as his lunch money. His utility function is given by the following utility function; U(X₁, X₂) = 6X₁X₂.

Can you help Tintin find hisoptimal "noodles-meatballs" consumption bundle? Before you do that, answer the following questions.

Ques. 1: Given Tintin's budget and the prices, how many servings of X₂can he buy if heonly chooses to buy X₂(i.e., if he chose X₁to be 0 units)?

a. X2 = 4

b. X2 = 6

c. X2 = 8

d. X2 = 12

Ques 2: Whattype of preferencesdoes Tintin have over dandanmian (X₁) and pearl meatballs (X₂)?

a. Tintin's utility function exhibits that the two dishes are perfect complements for him.

b. Tintin's utility function exhibits Cobb Douglas preferences

c. Tintin's utility function exhibits that the two dishes are perfect substitutes for him.

d. Tintin has lexicographic preferences for the two goods.

Ques 3: Given his utility function, what is Tintin'smarginal utility of increasing X₁by 1 unit when X₂= 1?

a. 2

b. 6

c. 3

d. 1/6

Ques. 4: What is themarginal utility of X₂when X₁= 1?

a. 2

b. 3

c. 6

d. 1/6

Ques. 5: Can you calculate the numerical value of Tintin'smarginal rate of substitutionfor the following values of X₁and X₂:

X₁= 1 and X₂= 1?

a. 2

b. 1/2

c. 6

d. 1