Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

BAX-400 – Foundations of Analytics

Linear Algebra Homework

Question 1:

Question 2:

Find the norm of the following vectors.

Question 3:

Find the unit vectors in the direction of the same vectors given below:

Question 4:

Find the distance between the following two vectors.

Question 5:

Find the dot product of the following vectors:

Question 6:

Find the angles between the following vectors:

Question 7:

Question 8:

Find the projection of v on u.

(25 points) Question 1:

The EZ Life Company manufactures sofas and armchairs in three models, A, B, and C. The company has regional warehouses in New York, Chicago, and San Francisco.

In its August shipment, the company sends 10 model-A sofas, 12 model-B sofas, 5 model-C sofas, 15 model-A chairs, 20 model-B chairs, and 8 model-C chairs to each warehouse.

a. Use a matrix to organize this information.

The September shipments from the EZ Life Company to the New York, San Francisco, and Chicago warehouses are given below.

b. Use a matrix to organize the September shipment information. What was the total amount shipped to the three warehouses in September?

The September sales for each model for the Chicago warehouse of the EZ Life Company is shown below.

c. Use a matrix to organize Chicago’s September shipment information.

d. What was the Chicago warehouse inventory on October 1, taking into account only the number of items received and sent out during the month?

(20 points) Question 2:

Microbucks Computer Company makes two computers, the Pomegranate II and the Pomegranate Classic, at two different factories. The Pom II requires 2 processor chips, 16 memory chips, and 20 vacuum tubes, while the Pom Classic requires 1 processor chip, 4 memory chips, and 40 vacuum tubes. Microbucks has in stock at the beginning of the year 500 processor chips, 5,000 memory chips, and 10,000 vacuum tubes at the Pom II factory and 200 processor chips, 2,000 memory chips, and 20,000 vacuum tubes at the Pom Classic factory. It manufactures 50 Pom IIs and 50 Pom Classics each month. Besides having the stock mentioned above, gets shipments of parts every month in the amounts of 100 processor chips, 1,000 memory chips, and 3,000 vacuum tubes at the Pom II factory and 50 processor chips, 1,000 memory chips, and 2,000 vacuum tubes at the Pom Classic factory. Find the company’s inventory of parts after 6 months, using matrix operations. Use matrix algebra.

(10 points) Question 3:

An investment firm recommends that a client invest in AAA, A, and B rated bonds. The average yield on AAA bonds is 6%, on A bonds 6.5%, and on B bonds 8%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond if the total investment is $25,000, and the investor wants an annual return of $1,650 on the three investments? Use matrix algebra.

(25 points) Question 4:

Two sectors of the U.S. economy are (1) lumber and wood products and (2) paper and allied products. In 1998 the input-output table involving these two sectors was as follows. (All figures are in millions of dollars.)

If external demand for lumber and wood products rises by $10,000 million and external demand for paper and allied products rises by $20,000 million, what increase in output of these two sectors is necessary? Use matrix algebra.

(10 points) Question 5:

Ever since Bob Misly was hired, things have been going awry at AllSmart CPAs Inc.. He has a tendency to lose important documents, especially around April, when tax returns of our business clients are due. Today Misly accidentally shredded Big Corp.’s investment records. We must therefore reconstruct them on the basis of the information he can gather. Bob recalls that the company earned an $8 million return on investments totaling $65 million last year. After a few frantic telephone calls to sources in Big Corp, he learned that Big Corp had made investments in four companies last year: A, B, C, and D. (For reasons of confidentiality their names are withheld.) Investments in company A earned 15% last year, investments in B depreciated by 20% last year, investments in C neither appreciated nor depreciated last year, while investments in D earned 20% last year. Misly was also told that Giant Corp invested twice as much in company A as in company C, and three times as much in company D as in company C. Does Misly have sufficient information to piece together Giant Corp’s investment portfolio before its tax return is due next week? If so, what does the investment portfolio look like?

(25 points) Question 6:

Aze Bookstore wants to ship books from its warehouses in Rancho Cordova and Fair Oaks to its stores, one in Folsom and another in Carmichael. Its warehouse in Rancho Cordova has 1,000 books, and its warehouse in Fair Oaks has 2,000. Each store orders 1,500 books. It costs $5 to ship each book from Rancho Cordova to Folsom and $1 to ship each book from Rancho Cordova to Carmichael. It costs $4 to ship each book from Fair Oaks to Folsom and $2 to ship each book from Fair Oaks to Carmichael. If Aze has a transportation budget of $9,000 and it is willing to spend all of it, how many books should Aze ship from each warehouse to each store to fulfill the demand. Use matrix algebra even if you think that you can solve this question without a pencil and a paper. You will be graded based on your matrix algebra code.

(20 points) Question 7:

Consider the following information about stocks of Corporations A, B, and C.

You invested a total of $8,400 in shares of the three stocks at the given prices and expected to earn $248 in annual dividends. If you purchased a total of 200 shares, how many shares of each stock did you purchase? Use matrix algebra.

(25 points) Question 1:

The human resource manager of a telemarketing firm is concerned about the rapid turnover of the firm’s telemarketers. It appears that many telemarketers do not work very long before quitting. There may be a number of reasons, including relatively low pay, personal unsuitability for the work, and the low probability of advancement. Because of the high cost of hiring and training new workers, the manager decided to examine the factors that influence workers to quit. He reviewed the work history of a random sample of workers who have quit in the last year and recorded the number of weeks on the job before quitting and the age of each worker when originally hired. Use regression analysis to describe how the work period and age are related. Dataset is available under Part 3 Question 1 CSV file.

(50 points) Question 2:

The CSV file Part 3 Question 2 CSV file contains monthly returns for four stocks – Merck (MRK), Proctor & Gamble (PG), Johnson & Johnson (JNJ), and Pfizer (PFE). Calculate the mean and standard deviation of the portfolio. The proportions invested in each stock are 25%.

Also shown on the dataset are monthly returns for four stocks – Boeing (BA), Home Depot (HD), Chevron (CVX), and Exxon (XOM). Calculate the mean and standard deviation of this portfolio. The proportions invested in each stock are 25%.

Which portfolio would a risk-averse investor choose? Which portfolio would a risk-taking investor choose?