Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $1800, and the cost required to set up the production line for the 6-cylinder connecting rods is $3300. Manufacturing costs are $15 for each 4-cylinder connecting rod and $20 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If there is a production changeover from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6200 6-cylinder connecting rods and 8400 4-cylinder connecting rods.

Let
x₄ = the number of 4-cylinder connecting rods produced next week
x₆ = the number of 6-cylinder connecting rods produced next week
s₄= 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
s₆ = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

1. Using the decision variables x₄ and s₄, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8400 units.
   
   x₄s₄
   
2. Using the decision variables x₆ and s₆, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 6200 units.
   
   x₆s₆
   
3. Write three constraints that, taken together, limit the production of connecting rods for next week.
   
   x₄s₄
   
   x₆s₆
   
   s₄ + s₆
   
4. Write an objective function for minimizing the cost of production for next week.
   
   Min x₄ + x₆ + s₄ + s₆

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 113 watts with a variance of 100. What is the probability that the mean amplifier output would be greater than 112.5 watts in a sample of 43 amplifiers if the claim is true?

HOW TO SOLVE IT ON TI-84?

A small airline has a policy of booking as many as 59 persons on an airplane that can seat only 51. (Past studies have revealed that only 80% of the booked passengers actually arrive for the flight.) Find the probability that if Air-USA books 59 persons, not enough seats will be available. (Show to 4 decimal places)

How would I solve this with my TI-84 calculator

1. Find the margin of error for the given values of​ c, sigma​, and c= 0.90​, sigma =2.3​, n= 49

2.

Use the confidence interval to find the margin of error and the sample mean.

(0.512,0.690)

3.

Find the minimum sample size n needed to estimate μ for the given values of​ c, σ​, and E. c=0.98​, σ=5.8​, and E =2

Assume that a preliminary sample has at least 30 members.

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area between z = 0.32 and z = 1.91 is ___.

There are several ways to describe data like the Histogram; what is the Histogram? Discuss how to use Excel to produce Histogram and what can you use it for?

What is descriptive statistics? How can you use descriptive statistics through Analysis Tool Pack add-in in Excel? Discuss how to use Descriptive Statistics to produce measures of center or dispersion? Can these be sued to support decision making? How?

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      H0:μ=82.7H0:μ=82.7
      H1:μ>82.7H1:μ>82.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=28n=28 with mean ¯x=93.7x¯=93.7 and a standard deviation of s=20.8s=20.8.

When finding the critical value and test statistic, which distribution would we be using?

• Normal distribution (invNorm for critical value)
• T distribution (invT for critical value)
• χ2χ2 distribution (invχχ for critical value)
• F distribution (invF for critical value)

6.73 Attitudes toward school. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 95, and the standard deviation is about 20. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score is ¯x = 103.3.

1. Assuming that σ = 30 for the population of older students, carry out a test of

   H₀: μ = 95

   H_a: μ > 95

   Report the P-value of your test, and state your conclusion clearly.

2. Your test in part (a) required two important assumptions in addition to the assumption that the value of σ is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?

Assume that the amount of time (hours) that young apprentices spend per week on their homework in their training program at a major manufacturer is normally distributed with a mean of 12 hours and a standard deviation of 5.

3. If 65 apprentices are selected at random, find the probability that they average more than 12 hours per week on homework.

a. 0.3999 b. 0.6999 c. 0.5000 d. 0.7999

4. If 65 apprentices are selected at random, find the probability that they average between 13 and 15 hours per week on homework.

a. 0.1534 b. 0.2534 c. 0.3333 d. 0.0534

The summary output of Paradise Retreats' model in Excel is in the tables below:

According to the tables, which of the following statements about this regression model are true?

Select all correct answers

A.The area of the apartment is not significant at a confidence level of 99%.

B.This regression model explains less than 50% of the variation of the price per night.

C.The area of the apartment is not significant at a confidence level of 95%.

D.The distance to the beach is not significant at a confidence level of 99%.

E.The area of the apartment is significant at a confidence level of 99%.

F.None of the above.

The bull and alternate hypothesis are:
Ho:u1<u2
H1:u1>u2
A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. use the 0.5 significant level.

Question text

An urban farmer is pondering whether to invest in ducks or chickens to raise for eggs that she plans to sell to friends and neighbors. The materials needed to make a good henhouse and chicken run cost $560. A simple setup for ducks is slightly higher, or $620, because they require water at all times. Ducklings and chicks are about the same in price—she figures that $20 is needed to get four females of either species. A 50-pound sack of layer pellets costs $14, and water is essentially free. It will take the four hens a month to work their way through the sack of feed and during that time she can collect 84 eggs. She plans to sell them for $5 per dozen. Ducks eat at the same rate but lay eggs at a higher rate—in one month she believes she can collect 108 eggs. Because duck eggs are more highly prized by consumers, the urban farmer believes they will sell for $6 per dozen.

1. Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. How many months after startup (assume that she buys mature birds that begin laying immediately) will profit from chickens equal profit from ducks?
2. Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. Plot profit lines for both ventures over a three-year period. Then, determine the range of output for when each venture is superior.

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and pre-preview ads before the movie starts. Many complain that the time devoted to previews is too long.† A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 6 minutes. Use that as a planning value for the standard deviation in answering the following questions. (Round your answers up to the nearest whole number.)

(a)

If we want to estimate the population mean time for previews at movie theaters with a margin of error of 105 seconds, what sample size should be used? Assume 95% confidence.

(b)

If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

A simple random sample with n=52 provided a sample mean of 24.0 and a sample standard deviation of 4.5.

a. Develop a 90% confidence interval for the population mean (to 1 decimal).

  ,  

b. Develop a 95% confidence interval for the population mean (to 1 decimal).

  ,  

c. Develop a 99% confidence interval for the population mean (to 1 decimal).

  ,  

d. What happens to the margin of error and the confidence interval as the confidence level is increased?

Q2: Problem 8: Capital Budgeting – 0,1 variable

Spencer Enterprises must choose among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next three years are summarized as follows:

Please develop and solve an integer programming model for maximizing the net present value.