Structuring a Make-or-Buy Problem

Fresh Foods, a large restaurant chain, needs to determine if it would be cheaper to produce 5,000 units of its main food ingredient for use in its restaurants or to purchase them from an outside supplier for $12 each. Cost information on internal production includes the following:

Fixed overhead will continue whether the ingredient is produced internally or externally. No additional costs of purchasing will be incurred beyond the purchase price.

Required:

1. What are the alternatives for Fresh Foods?
Make the ingredient in house or buy it externally.

2. List the relevant cost(s) of internal production and of external purchase.

All of the above

3. Which alternative is more cost effective?
Make the ingredient in-house

By how much?
$

4. Now assume that 20% of the fixed overhead can be avoided if the ingredient is purchased externally. Which alternative is more cost effective?
Buy

By how much?
$

Determining the Optimal Product Mix with One Constrained Resource

Comfy Fit Company manufactures two types of university sweatshirts, the Swoop and the Rufus, with unit contribution margins of $5 and $15, respectively. Regardless of type, each sweatshirt must be fed through a stitching machine to affix the appropriate university logo. The firm leases seven machines that each provides 1,000 hours of machine time per year. Each Swoop sweatshirt requires 6 minutes of machine time, and each Rufus sweatshirt requires 20 minutes of machine time.

Assume that there are no other constraints.

Required:

1. What is the contribution margin per hour of machine time for each type of sweatshirt? When computing your answers, round machine time per unit to two decimal places. Round your final answers to the nearest dollar.

2. What is the optimal mix of sweatshirts? If an amount is zero, enter "0".

3. What is the total contribution margin earned for the optimal mix?
$

Determining the Optimal Product Mix with One Constrained Resource and a Sales Constraint

Comfy Fit Company manufactures two types of university sweatshirts, the Swoop and the Rufus, with unit contribution margins of $5 and $15, respectively. Regardless of type, each sweatshirt must be fed through a stitching machine to affix the appropriate university logo. The firm leases seven machines that each provides 1,000 hours of machine time per year. Each Swoop sweatshirt requires 6 minutes of machine time, and each Rufus sweatshirt requires 20 minutes of machine time.

Assume that a maximum of 40,000 units of each sweatshirt can be sold.

Required:

1. What is the contribution margin per hour of machine time for each type of sweatshirt? When computing your answers, round machine time per unit to two decimal places. Round your final answers to the nearest dollar.

2. What is the optimal mix of sweatshirts? When computing your answers, round machine time per unit to two decimal places. Round your final answers to the nearest whole unit.

3. What is the total contribution margin earned for the optimal mix?
$

Last year Janet purchased a $1,000 face value corporate bond with an 7% annual coupon rate and a 20-year maturity. At the time of the purchase, it had an expected yield to maturity of 9.33%. If Janet sold the bond today for $1,091.83, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

Last year Janet purchased a $1,000 face value corporate bond with a 7% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 7.04%. If Janet sold the bond today for $1,004.41, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

Last year Janet purchased a $1,000 face value corporate bond with an 7% annual coupon rate and a 25-year maturity. At the time of the purchase, it had an expected yield to maturity of 13.17%. If Janet sold the bond today for $1,170.06, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

Last year Janet purchased a $1,000 face value corporate bond with an 7% annual coupon rate and a 20-year maturity. At the time of the purchase, it had an expected yield to maturity of 6.03%. If Janet sold the bond today for $1,080.57, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

The air temperature is measured every 6 hours for one week. The temperatures are given in the data table. Use the data to complete parts a through c below.

Data#   Temperature
1   42.8
2   55.6
3   41.3
4   44.6
5   43.4
6   58.5
7   46.1
8   45.6
9   41.6
10   59.9
11   51.1
12   46.3
13   54.6
14   56.2
15   54.9
16   43.2
17   51.7
18   51.8
19   49.8
20   47.4
21   46.2
22   55.2
23   51.9
24   41.3
25   50.2
26   59.8
27   49.3
28   48.4

a. Draw a systematic sample consisting of 2​ temperatures, and then calculate the sampling error for the sample.

The sampling error for the sample is ___degreesF. ​(Round to two decimal places as​ needed.)

b. Draw a systematic sample consisting of 4​ temperatures, and then calculate the sampling error for the sample.

The sampling error for the sample is ___degreesF. ​(Round to two decimal places as​ needed.)

c. Draw a systematic sample consisting of 7​ temperatures, and then calculate the sampling error for the sample.

The sampling error for the sample is negative _____degreesF. ​(Round to two decimal places as​ needed.)

Last year, those who took the LSAT test a second time score an average of 2.8 points higher than the first time. Suppose two independent and identically distributed random samples are drawn from this year’s exam: first-time and second-time LSAT takers.

a) Write the hypothesis test where the null is that the difference in scores between first- and second-time LSAT takers has not changed since last year and a two-sided alternative.
b) Suppose two independent random samples are drawn. One random sample contains the LSAT scores of first-time takers and has 25 observations and a sample variance of 256. The other random sample contains the LSAT scores of second-time takers and has 16 observations and a sample variance of 144. Derive the rejection rule at ! = 0.20 of the test in part a).

​(Constant dividend payout ratio policy​)

The Blunt Trucking Company needs to expand its fleet by 70 percent to meet the demands of two major contracts it just received to transport military equipment from manufacturing facilities scattered across the United States to various military bases. The cost of the expansion is estimated to be $11million. Blunt maintains a 40 percent debt ratio and pays out 50 percent of its earnings in common stock dividends each year.

a. If Blunt earns $4 million next​ year, how much common stock will the firm need to sell in order to maintain its target capital​ structure?

b. If Blunt wants to avoid selling any new stock but wants to maintain a constant dividend payout percentage of 50

​percent, how much can the firm spend on new capital​ expenditures?

a. If Blunt earns $4 million next​ year, how much common stock will the firm need to sell in order to maintain its target capital​ structure?

​$ million  ​(Round to two decimal​ places.)

b. If Blunt wants to avoid selling any new stock but wants to maintain a constant dividend payout percentage of

50 ​percent, how much can the firm spend on new capital​ expenditures?

​$ million  ​(Round to two decimal​ places.)

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail.

The sample mean is x = 12.2%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ = 11%; H₁: μ ≠ 11%; two-tailedH₀: μ = 11%; H₁: μ < 11%; left-tailed    H₀: μ ≠ 11%; H₁: μ = 11%; two-tailedH₀: μ = 11%; H₁: μ > 11%; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since n is large with unknown σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.