Ali, Bo, Cleo, and Dallas are picking their entrees at a restaurant. The choices are pasta, quesadillas, risotto, and sushi. They have some strict dietary preferences: 

• Cleo will not order sushi. 

• Ali and Bo want to steal each other’s food, so they will order different dishes. 

• Bo likes carbs, so he will only order pasta or risotto. 

• Cleo likes to be unique in her food orders and will not order the same dish as anybody else, with one exception: Ali and Cleo are actually twins, and always order the same dish as each other. 

• Dallas really dislikes quesadillas and will not order them. Answer the following questions for this situation: 

a. If we formulate this as a CSP with variables {A, B, C, D},e ach with domain {P, Q, R, S}, what are the constraints? 

b. We will run basic backtracking search to solve this CSP and make sure that every person (variable) is matched with their dream dish (value). We will select unassigned variables in alphabetical order, and we will also iterate over values in alphabetical order. What assignment will backtracking search return? 

c. Now assume that no values have been assigned to the variables and we will run one iteration of forward checking. What value(s) will be eliminated for which variables if we assign “pasta” to Ali?

d. Now assume we will solve the problem with local search using the min-conflicts algorithm. Assume we start with the initial assignment {A = P, B = P, C = P, D = P} and choose B as the variable to change. How many conflicts does the current value of B pose? What value for B would minimize the number of conflicts?