Use the Lagrange multiplier method to identify the stationary point(s) of the function ?(?, ?, ?)=10? + 5? + ? + 2?^2 + 4?? + ?^2 + 2?? - ?^2 - ??, subject to the constraint 5? + 3? + ? = 27. Subsequently determine the nature of the stationary point(s) using the bordered Hessian matrix.

A sample of size 27 will be drawn from a population with mean 4 and standard deviation 3.

(a) Is it appropriate to use the normal distribution to find probabilities for x?

(b) If appropriate find the probability that x will be greater than 2.

(c) If appropriate find the

40th percentile of x.

The following are distances (in miles) traveled to the workplace by 17 employees of a certain hospital.

What is The 25^th percentile?

What is the 70th percentile?

Problem 3.An exam has 30 multiple choice questions. Each question has five answer choices, ofwhich exactly one is correct. In how many different ways can a student who answers all questionsget at least 27 of them correct?

1) One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 3 will need an audit? 0.0151 0.9978 0.0109 0.9828

2) Sixty-seven percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months? 0.142 0.550 0.692 0.450

3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line? No, as the probability of six having the correct shape is not unusual Yes, as the probability of six having the correct shape is not unusual No, as the probability of six having the correct shape is unusual Yes, as the probability of six having the correct shape is unusual

1. If rice is an inferior, then:

1. A decrease in income causes increase in quantity demanded, shifts D curve to the right
2. A decrease in income causes increase in quantity demanded, shifts S curve to the right
3. A decrease in income causes increase in quantity demanded, shifts D curve to the left
4. A decrease in income causes increase in quantity demanded, shifts S curve to the left

2. Suppose a producer is able to separate customers into two groups, one having an inelastic demand and the other having an elastic demand. If the producer’s objective is to increase total revenue, he should:

1. Decrease the price charged to customer with the elastic demand and increase the price charged to customer with the inelastic demand
2. Increase the price for both groups of customers
3. Increase the price charged to customer with the elastic demand and decrease the price charged to customer with the inelastic demand
4. decrease the price for both groups of customers

3. Which of the following is likely to have the most price inelastic demand?

1. MP3 players
2. Laptop computers
3. Designer jeans
4. School fees for students

4. If chicken is a normal good, then:

1. An increase in income causes increase in quantity demanded, shifts D curve to the left
2. An increase in income causes increase in quantity demanded, shifts S curve to the left
3. An increase in income causes increase in quantity demanded, shifts D curve to the right
4. An increase in income causes increase in quantity demanded, shifts S curve to the right

The following were selected from among the transactions completed by Babcock Company during November of the current year:

Journalize the entries to record the transactions of Babcock Company for November using the periodic inventory system. Refer to the Chart of Accounts for exact wording of account titles.

Chart of Accounts

What are the five main differences between a Income statement that is produced by a for-profit company versus a local government Statements of Revenue, Expenditures and Changes in Fund Balances?

The Farr-Kroger Classic is a women’s professional golf tournament played each year in Ohio. Listed below are the total purse winnings (the amount of money that is distributed to the top golfers) and the prize for the winner for the 15 years from 1991 through 2005. The operators of this golf tournament believe that there is a relationship between the purse winnings and the prize and the prize is related to the purse winnings. In addition to the data provided, some of the possible linear regression relationships are provided.   These might be of help in your analysis.

Using linear regression relationships, answer the questions a) through c) below and on the following page.

a) Develop a projection for the amount of the prize for the winner for the year 2008 if the purse winnings for that year are projected to be $996,430. As part of your answer, include the independent and dependent variables and the accompanying linear regression relationship.

b) Now let’s suppose that we believe the prize for the winner is a function of time (dependent on time). Given this belief, develop a projection for the amount of the prize for the winner for the year 2008 and discuss your results compared to what you found in part a)

c) Would you recommend using the forecasts you found in parts a) and b) based on the strengths of the relationship? Why?