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Question : Bottles of SodaSlices of Pizza 51) The table above gives Ali’s : 1238693

Economics

 

 

Bottles of SodaSlices of Pizza

 

51) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. The price of pizza is $2 per slice and the price of soda is $1 per bottle. His marginal utility from the 4th slice of pizza is

A) 7.

B) 3.50.

C) 34.

D) 17.50.

E) 27.

 

52) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. The price of pizza is $2 per slice and the price of soda is $1 per bottle. His marginal utility from the 4th bottle of soda is

A) 21.

B) 3.

C) 3 units for soda ÷ 7 units for pizza.

D) 34.

E) 5.25.

53) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. The price of pizza is $2 per slice and the price of soda is $1 per bottle. Ali has $14 in his budget. When Ali maximizes his utility, how many bottles of soda does he buy?

A) fewer than 3

B) 3

C) 4

D) 5

E) more than 5

 

54) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. The price of pizza is $2 per slice and the price of soda is $1 per bottle. Ali has $14 in his budget. When Ali maximizes his utility, how many slices of pizza does he buy?

A) fewer than 2

B) 2

C) 3

D) 4

E) more than 4

 

55) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. The price of pizza is $2 per slice and the price of soda is $1 per bottle. Ali has $14 in his budget. When Ali maximizes his utility he buys ________ bottles of soda and ________ slices of pizza.

A) 4; 5

B) 6; 4

C) 2; 6

D) 6; 6

E) None of the above answers is correct.

56) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. The price of pizza is $2 per slice and the price of soda is $1 per bottle. Ali has $14 in his budget. When Ali maximizes his utility, his total utility equals

A) 6.

B) 9.

C) 69.

D) 61.

E) None of the above answers is correct.

 

57) The table above gives Ali’s total utility from consuming bottles of soda and slices of pizza. Suppose the price of a slice of pizza increases. As a result, Ali’s

A) marginal utility per dollar from pizza decreases.

B) total utility increases.

C) purchases of pizza might increase.

D) marginal utility from all the slices of pizza he consumes decreases.

E) marginal utility per dollar from soda increases.

 

 

58) Chase has a budget of $14 which he must allocate between steak and cranberry juice. The table gives his marginal utility and the marginal utility per dollar for both of those goods. The price of steak is $10 per serving and the price of cranberry juice is $2 per serving. To maximize his utility, Chase should buy

A) 2 servings of steak and 2 servings of cranberry juice.

B) 2 servings of steak and 4 servings of cranberry juice.

C) 1 serving of steak because this has the highest marginal utility.

D) 1 serving of steak and 2 servings of cranberry juice.

E) 4 servings of steak and 4 servings of cranberry juice.

 

 

 

59) Liz consumes two goods, candy bars and potato chips. Her budget is $4 per day. The price of a candy bar is $1.00 and the price of a bag of chips is 50 cents. Her utility is in the table above. How much marginal utility per dollar does the 3rd bag of potato chips give Liz?

A) 18

B) 4

C) 8

D) 36

E) We need more information to be able to answer the question.

60) Liz consumes two goods, candy bars and potato chips. Her budget is $4 per day. The price of a candy bar is $1.00 and the price of a bag of chips is 50 cents. Her utility is in the table above. For Liz to maximize her utility, what combination of candy bars and potato chips should she eat?

A) 4 candy bars and 0 bags of potato chips

B) 3 candy bars and 2 bags of potato chips

C) 2 candy bars and 4 bags of potato chips

D) 1 candy bar and 5 bags of potato chips

E) None of the above answers is correct.

 

 

 

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July 1, 2023
    

  

Artificial Intelligence

Exercise 1 : 

Which of the following are correct?

a. False |= True.

b. True |= False.

c. (A ∧ B) |= (A ⇔ B).

d. A ⇔ B |= A ∨ B.

e. A ⇔ B |= ¬A ∨ B.

f. (A ∧ B) ⇒ C |= (A ⇒ C) ∨ (B ⇒ C).

g. (C ∨ (¬A ∧ ¬B)) ≡ ((A ⇒ C) ∧ (B ⇒ C)).

h. (A ∨ B) ∧ (¬C ∨ ¬D ∨ E) |= (A ∨ B).

i. (A ∨ B) ∧ (¬C ∨ ¬D ∨ E) |= (A ∨ B) ∧ (¬D ∨ E).

j. (A ∨ B) ∧ ¬(A ⇒ B) is satisfiable.

k. (A ⇔ B) ∧ (¬A ∨ B) is satisfiable.

l. (A ⇔ B) ⇔ C has the same number of models as (A ⇔ B) for any fixed set of proposition symbols that includes A, B, C.

Exercise 2 : 

You have a number of trucks with which to deliver a set of packages. Each package starts at some location on a grid map, and has a destination somewhere else. Each truck is directly controlled by moving forward and turning. Construct a hierarchy of high-level actions for this problem. What knowledge about the solution does your hierarchy encode?

Exercise 3 : 25 Points

In your local nuclear power station, there is an alarm that senses when a temperature gauge exceeds a given threshold. The gauge measures the temperature of the core. Consider the Boolean variables A (alarm sounds), FA (alarm is faulty), and FG (gauge is faulty) and the multivalued nodes G (gauge reading) and T (actual core temperature).

a. Draw a Bayesian network for this domain, given that the gauge is more likely to fail when the core temperature gets too high.

b. Is your network a polytree? Why or why not?

c. Suppose there are just two possible actual and measured temperatures, normal and high; the probability that the gauge gives the correct temperature is x when it is working, but y when it is faulty. Give the conditional probability table associated with G.

d. Suppose the alarm works correctly unless it is faulty, in which case it never sounds. Give the conditional probability table associated with A.

e. Suppose the alarm and gauge are working and the alarm sounds. Calculate an expression for the probability that the temperature of the core is too high, in terms of the various conditional probabilities in the network.

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July 1, 2023
    

  

Artificial Intelligence

Exercise 1 : 

Which of the following are correct?

a. False |= True.

b. True |= False.

c. (A ∧ B) |= (A ⇔ B).

d. A ⇔ B |= A ∨ B.

e. A ⇔ B |= ¬A ∨ B.

f. (A ∧ B) ⇒ C |= (A ⇒ C) ∨ (B ⇒ C).

g. (C ∨ (¬A ∧ ¬B)) ≡ ((A ⇒ C) ∧ (B ⇒ C)).

h. (A ∨ B) ∧ (¬C ∨ ¬D ∨ E) |= (A ∨ B).

i. (A ∨ B) ∧ (¬C ∨ ¬D ∨ E) |= (A ∨ B) ∧ (¬D ∨ E).

j. (A ∨ B) ∧ ¬(A ⇒ B) is satisfiable.

k. (A ⇔ B) ∧ (¬A ∨ B) is satisfiable.

l. (A ⇔ B) ⇔ C has the same number of models as (A ⇔ B) for any fixed set of proposition symbols that includes A, B, C.

Exercise 2 : 

You have a number of trucks with which to deliver a set of packages. Each package starts at some location on a grid map, and has a destination somewhere else. Each truck is directly controlled by moving forward and turning. Construct a hierarchy of high-level actions for this problem. What knowledge about the solution does your hierarchy encode?

Exercise 3 : 25 Points

In your local nuclear power station, there is an alarm that senses when a temperature gauge exceeds a given threshold. The gauge measures the temperature of the core. Consider the Boolean variables A (alarm sounds), FA (alarm is faulty), and FG (gauge is faulty) and the multivalued nodes G (gauge reading) and T (actual core temperature).

a. Draw a Bayesian network for this domain, given that the gauge is more likely to fail when the core temperature gets too high.

b. Is your network a polytree? Why or why not?

c. Suppose there are just two possible actual and measured temperatures, normal and high; the probability that the gauge gives the correct temperature is x when it is working, but y when it is faulty. Give the conditional probability table associated with G.

d. Suppose the alarm works correctly unless it is faulty, in which case it never sounds. Give the conditional probability table associated with A.

e. Suppose the alarm and gauge are working and the alarm sounds. Calculate an expression for the probability that the temperature of the core is too high, in terms of the various conditional probabilities in the network.

default image
July 1, 2023
    

  

Artificial Intelligence

Exercise 1 : 

Which of the following are correct?

a. False |= True.

b. True |= False.

c. (A ∧ B) |= (A ⇔ B).

d. A ⇔ B |= A ∨ B.

e. A ⇔ B |= ¬A ∨ B.

f. (A ∧ B) ⇒ C |= (A ⇒ C) ∨ (B ⇒ C).

g. (C ∨ (¬A ∧ ¬B)) ≡ ((A ⇒ C) ∧ (B ⇒ C)).

h. (A ∨ B) ∧ (¬C ∨ ¬D ∨ E) |= (A ∨ B).

i. (A ∨ B) ∧ (¬C ∨ ¬D ∨ E) |= (A ∨ B) ∧ (¬D ∨ E).

j. (A ∨ B) ∧ ¬(A ⇒ B) is satisfiable.

k. (A ⇔ B) ∧ (¬A ∨ B) is satisfiable.

l. (A ⇔ B) ⇔ C has the same number of models as (A ⇔ B) for any fixed set of proposition symbols that includes A, B, C.

Exercise 2 : 

You have a number of trucks with which to deliver a set of packages. Each package starts at some location on a grid map, and has a destination somewhere else. Each truck is directly controlled by moving forward and turning. Construct a hierarchy of high-level actions for this problem. What knowledge about the solution does your hierarchy encode?

Exercise 3 : 25 Points

In your local nuclear power station, there is an alarm that senses when a temperature gauge exceeds a given threshold. The gauge measures the temperature of the core. Consider the Boolean variables A (alarm sounds), FA (alarm is faulty), and FG (gauge is faulty) and the multivalued nodes G (gauge reading) and T (actual core temperature).

a. Draw a Bayesian network for this domain, given that the gauge is more likely to fail when the core temperature gets too high.

b. Is your network a polytree? Why or why not?

c. Suppose there are just two possible actual and measured temperatures, normal and high; the probability that the gauge gives the correct temperature is x when it is working, but y when it is faulty. Give the conditional probability table associated with G.

d. Suppose the alarm works correctly unless it is faulty, in which case it never sounds. Give the conditional probability table associated with A.

e. Suppose the alarm and gauge are working and the alarm sounds. Calculate an expression for the probability that the temperature of the core is too high, in terms of the various conditional probabilities in the network.

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