Question 3

The Fly-High Airplane Company builds small jet airplanes to sell to corporations for use by their executives. To meet the needs of these executives, the company's customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes.

Fly-High has recently received purchase requests from three customers with short deadlines. However, because the company's production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers.

The relevant data are given in the table below. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once production is under way, the marginal net revenue from each airplane produced is shown in the second row. The marginal net revenue is the purchase price minus the marginal production cost. The third row gives the percentage of the available production capacity that would be used for each plane produced. The last row indicates the maximum number of airplane requested by each customer (but less will be accepted).

Fly-High now wants to determine how many airplanes to produce for each customer (if any) to maximize the company's total profit (total net revenue minus start-up costs). Formulate the mixed integer programming model and solve it using Excel solver for this problem.

(Also how to solve on ti-84)

1.

Fuel efficiency. Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). One of the authors of this book conducted an experiment with his 2006 Toyota Highlander Hybrid by randomly recording mpg readings shown on the vehicle computer while the car was set to 60 miles per hour by cruise control. Here are the mpg values from the experiment:

Sigma, σ, is unknown.

What is the standard error of the mean? (use 3 decimal places)

What is the 98% confidence interval for the mean mpg? [ mpg, mpg] (use 2 decimal places)

Question 2.

Intergalactic Software Company went public three months ago. You are a sophisticated investor who devotes time to fundamental analysis as a way of identifying mispriced stocks.

1)Which of the following characteristics would you focus on in deciding whether to follow this stock?

• Market capitalization
• The average number of shares traded per day
• The bid-ask spread for the stock
• Whether the underwriter that brought the firm public is a top tier investment banking firm
• Whether the firm’s audit company is a Big Four firm
• Whether there are analysts from major brokerage firms following the company
• Whether the stock is held mostly by retail or by institutional investors

2) When you looked at the projection for Intergalactic Software Company’s revenue in the future, you found that most of analysts assume the revenue growth rate is mean-reverting over time. What is the rationale to assume that revenue growth rate is mean-reverting over time?

For many years, Lawton Industries has manufactured prefabricated houses where the houses are constructed in sections to be assembled on customers’ lots. The company expanded into the precut housing market in 2006 when it acquired Presser Company, one of its suppliers. In this market, various types of lumber are precut into the appropriate lengths, banded into packages, and shipped to customers’ lots for assembly. Lawton decided to maintain Presser’s separate identity and, thus, established the Presser Division as an investment center of Lawton.

              Lawton uses return on average investment (ROI) as a performance measure the investment defined as operating assets employed. Management bonuses are based in part on ROI. All investments in operating assets are expected to earn a minimum return of 15% before income taxes. Presser’s ROI has ranged from 19.3% to 22.1% since it was acquired in 2006. The division had an investment opportunity in the year just ended that had an estimated ROI of 18%, but Presser’s management decided against the investment because it believed the investment would decrease the division’s overall ROI.

              Presser’s operating statement for the year just ended is presented next. The division’s operating assets employed were $12,600,000 at the end of the year, a 5% increase over the balance at the end of the previous year.

_______________________________________________________________________

                                                          Presser Division Operating Statement

                                                                  For the year ended Dec. 31

                                                                             ($000 omitted)

_______________________________________________________________________

              Sales Revenue                                                                                                                   $24,000

              Cost of Goods Sold                                                                                                              15,800

                   Gross Profit                                                                                                                      $8,200

              Operating Expenses

              Administrative                                                                          $2,140

              Selling                                                                                         3,600                              5,740

              Income from operations

                   Before income taxes                                                                                                      $2,460

_______________________________________________________________________

Questions

1. Calculate these performance measures for the year just ended for the Presser Division of Lawton Industries:

1. Return on average investment in operating assets employed (ROI).
2. Residual income calculated on the basis of average operating assets employed.

2. Would the management of Presser Division have been more likely to accept the investment opportunity it had during the year if residual income were used as a performance measure instead of ROI? Explain your answer.

The Presser Division is a separate investment center with Lawton Industries. Identify and describe the items Presser must control if it is to be evaluated fairly by either the ROI or residual income performance measures

Step 4:

What percent of the variation in corn yield is explained by these two variables? Give your answers to 2 decimal places and do not include units in your answers.

Percent explained by the model = %

Step 5:

Using the regression equation, find a point estimate for the corn yield for 2014 Assume that the soy bean yield for that year is 42.

Point Estimate = (Give your answer to 1 decimal place.)

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4
23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5
27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7
52      2008    153.9   39.7
53      2009    164.7   44.0
54      2010    152.8   43.5
55      2011    147.2   41.9
56      2012    123.4   39.8
57      2013    158.8   43.3

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4

23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5

27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7

Use both predictors. From the previous two exercises, we conclude that year and soybean may be useful together in a model for predicting corn yield. Run this multiple regression.

a)       Explain the results of the ANOVA F test. Give the null and alternate hypothesis, test statistic with degrees of freedom, and p-value. What do you conclude?

b)      What percent of the variation in corn yield in explained by these two variables? Compare it with the percent explained in the previous simple linear regression models.

c)       State the regression model. Why do the coefficients for year and soybean differ from those in the previous exercises?

d)      Summarize the significance test results for the regression coefficients for year and soybean yield.

e)      Give a 95% confidence interval for each of these coefficients.

f)        Plot the residual versus year and soybean yield. What do you conclude?

E6-35. Evaluating Grocery Stores Using Efficiency Ratios

Below are data for three publicly traded grocery stores that range in size from local (Village Super Markets) to regional (Publix) to national (Kroger). Use the ratios below to answer the requirements. Assume

that the companies sell roughly the same mix of products and face about the same inventory costs.

Fiscal 2018 Publix Kroger Village Super Market

Gross profit margin %. . . . . . . . . . . . . . . . . . . 29.6% 21.7% 27.2%

Number of stores at year-end. . . . . . . . . . . . . 1,211 2,764 30

Sales ($ per square foot) . . . . . . . . . . . . . . . . $639 $677 $1,165

Sales per store ($ millions). . . . . . . . . . . . . . . $ 30 $ 44 $ 54

Average store size (thousand square feet). . . 47 65 46

COGS (per square foot) . . . . . . . . . . . . . . . . . $450 $530 $ 848

Days inventory outstanding . . . . . . . . . . . . . . 26.5 25.7 12.6

Required

a. On average, which company has the freshest food?

b. Which company is least efficient with its space?

c. Which company has the lowest prices?

d. Which company is busiest?

e. Which company has the smallest stores