College grades company... Question:

A group of recent college grads decides to open a new airline company called BAir. They buy one airplane that has ?

seats. They estimate that two types of travelers will purchase tickets for a certain flight on a certain date:

Leisure travelers, who are willing to pay only the discounted fare $?

Business travelers, who are willing to pay the full fare $? (where ?>?).

After quite a bit of market research, they conclude that the number of leisure travelers requesting tickets for this flight will be greater than ?

n for sure, while the number of business travelers requesting tickets is random. Please assume that the leisure travelers always purchase their tickets before the business travelers do. (In practice, this is roughly true, which is why airfares increase as the flight date gets closer).

BAir wishes to sell as many seats as possible to business travelers since they are willing to pay more. However, since the number of such travelers is random and these customers arrive near the flight's departure date, a sensible strategy is for BAir to allocate a certain number of seats ? for full fares and the remainder, ??? for discount fares.

The discount fares are sold first: The first ??? customers requesting tickets will be charged $? per ticket and the remaining (at most ?) customers will be offered the full price $? . Since leisure travelers are only willing to pay $? , they will decline to buy a full-fare ticket. Thus, if there are less than ? ticket requests from business travelers, some seats will not be sold (and BAir regrets not selling them to leisure travelers). Conversely, it is possible that some of the seats sold to leisure travelers for $? could have been sold to business travelers who would have been willing to pay $? .

Question 1

Show that the problem of finding the optimal number of full-fare seats, ? , is equivalent to a newsvendor problem. Clearly define the underage cost, overage cost, and uncertainty. What is the critical ratio?

Question 2

Suppose that demand for full-fare seats is normally distributed with a mean of 40 and a standard deviation of 18 (thus ? = 40 and ? = 18). There are ?=100 seats on the flight and the fares are ?=$175 and ?=$400 . What is the optimal number of full-fare seats? (Fractional solutions are OK)

Question 3

For each situation below, explain how the underage cost and the overage cost will change. How will this affect the optimal quantity reserved for full-fare customers? (No need to recalculate the optimal quantity - a qualitative answer is sufficient)

Situation 1: The full-fare tickets are fully refundable and, with some probability, each business traveler will cancel his or her ticket at the last minute, too late for BAir to re-sell the newly vacant seat.

Situation 2: Any unsold seats may be sold at the very last minute for a steeply discounted price, $? (?). These tickets are made available after the business travelers have requested tickets.

[4/7, 08:50] Kiprutoh: Question:

At whatever point a driver experiences slowing down issues, particularly an erratic pulling aside, the scoundrel is constantly held to be the brake cushion. Minor components, particularly titanium, can consolidate with different components to shape minute particles of titanium carbonitride which change the level of grating between the cushion and circle and lead to inconsistent wear. The level of titanium in a brake cushion ought not surpass 5%. An investigation is led to distinguish a circumstance in which the mean level of titanium in the brake cushions being delivered by a specific producer surpasses 5%.

(a) Set up the proper invalid and altemative theories.

(b) Examine the down to earth outcomes of making a Sort I and a Sort II blunder.

(c)A test of 100 brake cushions yields a mean level of x = .051. Expect to be that a = .008. Discover the P an incentive for the test. Do you imagine that Hs ought to be dismissed? Clarify. To what exactly kind of mistake would you say you are presently subject?

Question 82

The current particulate norm for diesel vehicle discharge is .6 g/mi. It is trusted that another motor plan has decreased the outflows to a level beneath this norm. (a) Set up the suitable invalid and altemative theories for affirming that the new motor has a mean emanation level beneath the current norm.

(b) Talk about the reasonable results of making a Sort I and a Sort II blunder.

(c) An example of 64 motors tried yields a mean discharge level of = .5 g/mi. Expect to be that a = .4. Discover the P estimation of the test. Do you believe that Ho ought to be dismissed? Clarify. To what exactly kind of mistake would you say you are currently subject?

Question 83

It is imagined that over 15% of the heaters used to deliver steel in the US are as yet open-hearth heaters. To confirm this conflict. an arbitrary example of 40 heaters is chosen and analyzed.

(a) Set up the proper invalid and elective theories needed to help the expressed dispute.

(b) When the information are accumulated, it is tracked down that 9 of the 40 heaters investigated are open-hearth heaters. Utilize the typical estimate to the binomial dissemination (Sec. 4.6) to discover the P an incentive for the test. Do you believe that Hs ought to be dismissed? Clarify. To what in particular sort of blunder would you say you are currently subject? Hypothesis 4.6.1 (Typical guess to the binomial circulation). Leave X alone binomial with boundaries n and p. For enormous n. Xis roughly typical with mean np and change np(1 - p).

Question 84

It is realized that faulty things will be created even on mechanized mechanical production systems. A specific cycle regularly creates 5% defectives. Assuming the extent of defectives surpasses 5%, the line should be closed down and changed.

(a) Set up the suitable invalid and altemative speculations expected to recognize a circumstance in which the extent of defectives delivered surpasses .05.

(b) Examine the viable results of submitting a Sort I and a Sort II mistake.

(c) An irregular example of 100 things is chosen and tried. Of these, 7 are discovered to be faulty. Utilize the ordinary estimate to the binomial circulation to discover the P estimation of the test. Do you believe that Ha ought to be dismissed?

3. A yoga studio opens a site in a small town. As the only yoga studio in its market, it would have market power, i.e. to sell larger quantities, it would have to set lower prices. (a) The demand curve for memberships at the studio is P = 30- -Q for Q 300 where Q denotes number of memberships and P the price. Draw the demand curve for memberships at the in the (Q, P) co-ordinates (Q on horizontal axis). How many memberships can be sold at P = 20? (b) The fixed cost of running the studio is 700. A yoga instructor costs 300 to hire and each instructor can serve up to 50 members. Draw the cost curve for the gym. (c) Draw the average cost curve for the studio. Is it possible to operate the studio profitably? (d) What is the optimal price for a profit maximizing studio? How many instructors should be hired? (Hint: What is the marginal revenue for the studio?).133 35 43 51 651 QUESTION 69 Nelson Corporation has the following information available for 2009 Cash balance on 1/1/2009 $3.000 Cash balance on 12/31/2009 5.000 Net cash provided by operating activities 75,000 Net cash utilized by investing activities 80.000 The "handing activity section of Nelson's statement of cash flows would show Net cash provided by financing activities of $5,000. Net cash ullized by financing activities of 52,000 Net cash utilized by financing activities of $3.000. Net cash provided by financing activities of $7 000 QUESTION 70