1) Considerthe demand for a public good estimated for two sets of consumers:

(1) P1 = -0.5Q +10

(2) P2 = -0.25Q + 5

where Pis the price that each consumer is willing to pay at difference levels ofquantity. The cost of providing one additional unit of this public good is $4(e.g., marginal cost (MC) = $4)

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1. Construct a linear program consisting of N inequalities on two variables for • which the simplex algorithm requires at least N /2 pivots.

2. Give a three-dimensional linear-programming problem that illustrates the difference between the greatest-increment and steepest-descent column-selection methods.

3. Modify the implementation given in the text to write out the coordinates of the optimal solution point.

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1. Consider the marginal probability over C2 = {A1,2, A2,2, A3,2, A4,2} in the 4 × 4 grid network. Show that, if we assume general potentials, this marginal probability does not satisfy any conditional independencies.

2. Consider a clique tree T that is constructed from a run of variable elimination over a Gibbs distribution P’Φ, as described in section 10.1.2. Let Si,j be a sepset in the clique tree. Show that, for general potentials, P’Φ does not satisfy any conditional independencies relative to the marginal distribution over Si,j.

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1. Consult one or more of the references for software heuristics. Extract several heuristics and use them to evaluate a software-intensive system.

2. Requirements defects that are delivered to customers are the most costly because of the likelihood they will require extensive rework. But discovering such defects anytime before customer delivery is likewise very costly because only the customers’ reaction may make the nature of the defect apparent. One approach to this problem is prototyping to get early feedback. How can software be designed to allow early prototyping and feedback of the information gained without incurring the large costs associated with extensive rework?

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1) Contract Law – Insurance Mario has purchased a new kart, and would like to get some insurance on it. The kart is worth $1,000, and there is a 10% chance he will be in an accident and do $500 worth of damage to his kart. Mario’s utility function is U(V) = ln(V), where V is the value of his kart. a) Calculate Mario’s expected utility with no insurance. b) Now suppose Mario can buy auto insurance from Yoshi for a premium of $I that will completely compensate him for his $500 loss if it occurs. Find an expression Mario’s expected utility with insurance. c) What is the most Mario is willing to pay for insurance? d) Repeat steps a) – c) with a utility function of U(V) = V. Comment on why any differences are present in willingness to pay for insurance.

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