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- Suppose one canoe rents for 40,and2 is taken off the price for each additional canoe rented by a ground. What size group gives the most income? Assume that there are 20 canoes available.Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γ E[I], where γ >1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1. [Hint: draw a coordinate plane with p on the x-axis and M on the y-axis.] Based on this graph, under what conditions is she least likely to buy the subsidized insurance?a pollster wnats to minimize the effect the order of the questions has on a person's response to a survey. how many different surveys are required to cover all possible arrangements if there are 9 questions on the survey?
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- The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.The number of oil changes per hour at Quick Lube is described by the following short-term production function: Q=10L−0.5L2 If oil changes (Q) sell for $20 each and labor (L) costs $40 per hour (wage), what is the optimal number of units of labor to hire per hour? How many oil changes will be completed?Suppose that in solving a TSP you use the nearest-neighboralgorithm and find a nearest-neighbor tour with a total costof $13,500. Suppose that you later find out that the cost ofan optimal tour is $12,000. What was the relative error ofyour nearest-neighbor tour? Express your answer as a percentage,rounded to the nearest tenth of a percent.
- A farmer can get 2 dollars per bushel for their potatoes on July 1. After July 1, the pricedrops by 2 cents per bushel per extra day. On July 1, a farmer had 80 bushels ofpotatoes in the field and estimates that the crop is increasing at the rate of 1 bushel perday. When should the farmer harvest the potatoes to maximize his revenue?[Hint: Let ?? be the number of extra day after July 1 and ?? be the revenue.]Suppose that you randomly selected 26 adults. Assume 17% of the population smoke. Round all answers to 2 decimal places.a) Using the Range Rule of Thumb, what is the minimum number of usual smokers we can expect to get out of 26 adults?b) Using the Range Rule of Thumb, what is the maximum number of usual smokers we can expect to get out of 26 adults?c) Would it be unusual to randomly select 26 adults and get 10 smokers? Yes, since 10 is not between the maximum and minimum usual values. No, since 10 is between the maximum and minimum usual values.A 60 room hotel is filled to capacity every night at a rate of $40 per room. The management wants to determine if a rate increase would increase their profit. They are not interested in a rate decrease. Suppose management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. If each rented room costs $8 a day to service, how much should the management charge per room to maximize profit?