Most frequent pattern mining algorithms consider only distinct items in a transaction. however, multiple occurrences of an item in the same shopping basket, such as four cakes and three jugs of milk, can be important in transactional data analysis. how can one mine frequent itemsets efficiently considering multiple occurrences of items? propose modifications to the well-known algorithms, such as apriori and fp-growth, to adapt to such a situation.

If a company’s employees are angry about their work, a visiting auditor may also become agitated, illustrating the power of

Consider the local telephone company, a natural monopoly. the following graph shows the monthly demand curve for phone services and the company’s marginal revenue (mr), marginal cost (mc), and average total cost (atc) curves. 0 2 4 6 8 10 12 14 16 18 20 100 90 80 70 60 50 40 30 20 10 0 price (dollars per subscription) quantity (thousands of subscriptions) d mr mc atc 8, 60 suppose that the government has decided not to regulate this industry, and the firm is free to maximize profits, without constraints. complete the first row of the following table. pricing mechanism short run long-run decision quantity price profit (subscriptions) (dollars per subscription) profit maximization marginal-cost pricing average-cost pricing suppose that the government forces the monopolist to set the price equal to marginal cost. complete the second row of the previous table. suppose that the government forces the monopolist to set the price equal to average total cost. complete the third row of the previous table. under average-cost pricing, the government will raise the price of output whenever a firm’s costs increase, and lower the price whenever a firm’s costs decrease. over time, under the average-cost pricing policy, what will the local telephone company most likely do

"in my opinion, we ought to stop making our own drums and accept that outside supplier's offer," said wim niewindt, managing director of antilles refining, n.v., of aruba. "at a price of $21 per drum, we would be paying $4.70 less than it costs us to manufacture the drums in our own plant. since we use 70,000 drums a year, that would be an annual cost savings of $329,000." antilles refining's current cost to manufacture one drum is given below (based on 70,000 drums per year):