Manuel and poornima are building their portfolios. manuel purchases shares in a mutual fund and pays fees to a manager who actively manages the mutual fund's portfolio. he does so because he believes that the manager can identify inexpensive stocks that will rise in value. poornima is not convinced. she buys shares in an index fund-a type of mutual fund that simply buys all of the stocks in a given stock index rather than actively managing a portfolio. manuel builds his portfolio on the supposition that: the stock market exhibits informational efficiency. stock analysts can use fundamental analysis to identify undervalued stocks. stock prices follow a random walk.

Needs to schedule the staffing of the center. it is open from 8am until midnight. larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required: time of dayminimum number of consultants required to be on duty8 am-noon4noon-4 pm84pm-8pm108pm-midnight6 two types of computer consultants can be hired: full-time and part-time. the full- time consultants work for eight consecutive hours in any of the shifts: morning (8am- 4pm), afternoon (noon-8pm) and evening (4pm-midnight). full-time consultants are paid $14 per hour. part-time consultants can be hired to work any of the four shifts listed in the table. part-time consultants are paid $12 per hour. an additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. formulate this as an lp problem. you must define your variables clearly

mark, a civil engineer, entered into a contract with david. as per the contract, mark agreed to design and build a house for david for a specified fee. mark provided david with an estimation of the total cost and the contract was mutually agreed upon. however, during construction, when mark increased the price due to a miscalculation on his part, david refused to pay the amount. this scenario is an example of a mistake.

At a student café, there are equal numbers of two types of customers with the following values. the café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate). students with early classes students without early classes coffee 70 60 banana 51 101 the marginal cost of coffee is 10 and the marginal cost of a banana is 40. the café owner is considering three pricing strategies: 1. mixed bundling: price bundle of coffee and a banana for 161, or just a coffee for 70. 2. price separately: offer coffee at 60, price a banana at 101. 3. bundle only: coffee and a banana for 121. do not offer goods separately. assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle. for simplicity, assume there is just one student with an early class, and one student without an early class. price strategy revenue from pricing strategy cost from pricing strategy profit from pricing strategy 1. mixed bundling $ $ $ 2. price separately $ $ $ 3. bundle only $ $ $ pricing strategy yields the highest profit for the café owner.