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 by X1, and the price of one serving to be 3 Chinese yuan.

Let one serving of pearl meatballs be denoted by X2 and the price of one serving to be 4 Chinese yuan.

Tintin has 24 yuan available as his lunch money. His utility function is given by the following utility function; U(X1, X2) = 6X1X2.

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

1- Can you calculate the numerical value of Tintin's marginal rate of substitution for the following values of X1 and X2:

X1 = 1 and X2 = 1?

2-What is theslopeof Tintin'sbudgetline?

3- If Tintin ends up choosing2 bowls of noodles (X1)and2 servings of meatballs (X2), do you think he will be able tomaximizehis utility level?

4- With the help of your knowledge of microeconomic theory, can you find the consumption bundle that willmaximize Tintin's utilityfrom his lunch?