RS p.1.c. manufactures domestic food mixers. It is investigating whether or not to accept a three-year contract to make a new model for sale through a supermarket chain. The contract uses skilled labour which cannot be increased above that currently available and RS p.1.c. will receive a fixed price of £42 per mixer for all the mixers it can produce in the three-year period. The following estimates have been made:

Capital investment £50000 payable now, with nil scrap value.

Additional overhead £25000 per annum.

Materials £30 per mixer Labour £6 per hour.

The factory manager knows from experience of similar machines that there will be a learning effect for labour. He estimates that this will take the form:

y = ax^-0.3

where y = average labour hours per unit

a = labour hours for first unit

x = cumulative production

He estimates that the first mixer will take 10 hours to produce and that the fixed amount of labour available will enable 5000 mixers to be produced in the first year. Apart from the capital investment, all cash flows can be assumed to arise at year ends. The company has a cost of capital of 15%.

Conduct a sensitivity analysis to support the decision-making process.

Deleon Inc. is preparing its annual budgets for the year ending December 31, 2020. Accounting assistants furnish the data shown below.

An accounting assistant has prepared the detailed manufacturing overhead budget and the selling and administrative expense budget. The latter shows selling expenses of $662,000 for product JB 50 and $365,000 for product JB 60, and administrative expenses of $543,000 for product JB 50 and $342,000 for product JB 60. Interest expense is $150,000 (not allocated to products). Income taxes are expected to be 30%.

An experiment was conducted to investigate the effect of extrusion pressure (P) and temperature at extrusion (T) on the strength y of a new type of plastic. Two plastic specimens were prepared for each of five combinations of pressure and temperature. The specimens were then tested in a random order and the breaking strength for each specimen was recorded. The independent variables were coded (transformed) as follows to simplify the calculations: x₁= (P-200)/10, x₂= (T-400)/25. The n=10 data points are listed in the table:

                y                     X₁                  X₂

              5.2                  -2                  2

                5                  -2                  2

              0.3                  -1                 -1

            -0.1                  -1                 -1

            -1.2                   0                  -2

            -1.1                   0                  -2

              2.2                  1                  -1

2                   1                  -1

6.2________2 ________2

              6.1                  2                   2

!                                                               

1. Find the least-squares regression equation of the form y = β₀ + β₁x₁ + β₂x₂ + ε (you may use a calculator or any software that can perform operations with matrices).
2. Does the model contribute information for the prediction of y? Test using α=0.10.
3. Suppose that we are interested in an interval estimate for the strength of plastic for the following combination of pressure and temperature: x₁=1 and x₂=1. Would a confidence interval or a prediction interval be more appropriate in this situation? Calculate this interval using α=0.01.

1) What term describe the region in space where there is a high probability of finding an electron?

a) Quantum

b) Dimension

c) Configuration

d) Orbital

2. Using the bronsted-lowry theory of acids and bases, what is the conjugate acid of HSO4?

a) H2SO4

b) 2HSO4

c) HSO4

d) SO42

3.) How is the atomic mass of any element calculated?

a) Protons plus electron

b) Protons plus neutrons

c) Electrons plus neutrons

d) It is the number of protons

4.) A one-liter balloon is composed of 0.5 mole of helium gas, what volume will 1.8 moles of helium occupy at the same temperature and pressure?

a) 4.2 liters

b) 3.6 liters

c) 0.6 liters

d) 0.3 liters

5.) What biochemical compound, produced during cellular respiration, is used as the energy currency of the cell?

a) Glycogen

b) Acetic acid

c) Lactic acid

d) Adenosine triphosphate

6.) What is the correct characteristic of nitrogen?

a) Have 10 neutrons.

b) Is a nonmetal

c) Exists in nature as monoatomic gas

d) Has 9 electrons.

7.) What type of biochemical molecule contains two or more amino acids joined by peptide bonds?

a) Protein

b) Lipids

c) Carbohydrate

d) Nucleic acid

Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H0: p = 0.5 versus Ha: p ≠ 0.5 based on a random sample of 25 individuals. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X.

(b) Suppose that x = 5. Which other values of X are at least as contradictory to H0 as this one? (Enter your answers as a comma-separated list.)

Use it to compute the P-value when

x = 5.  (Round your answer to three decimal places.)

(d)

If H₀ is to be rejected when P-value ≤ 0.044,

compute the probability of a type II error when

p = 0.4,

again when

p = 0.3,

and also when

p = 0.6

and

p = 0.7.

[Hint:

P-value > 0.044

is equivalent to what inequalities involving x? Keep in mind that

P(type II error when p = 0.4) = P(H₀ is not rejected when p = 0.4).]

(Round your answers to three decimal places.)

p = 0.4p = 0.3p = 0.6p = 0.7

Sampling Distributions

This exercise is to be completed in a group.

For the population: 1 3 5 7 9

Find the mean and standard deviation.

Mean Calculation:

1 + 3 + 5 + 7 + 9 = 25

25 / 5 = 5

The mean is 5

Standard Deviation Calculation:

( 1 - 5 ) ² = ( -4 ) ² = 16

( 3 - 5 ) ² = ( -2 ) ² = 4

( 5 - 5 ) ² = ( 0 ) ² = 0

( 7 - 5 ) ² = ( 2 ) ² = 4

( 9 - 5 ) ² = ( 4 ) ² = 16

16 + 4 + 0 + 4 + 16 = 40

( 1 / 5 ) × 40 = 8

√( 8 ) = 2.8284

The standard deviation is ≈ 2.83

Now determine how many samples of size 2 can be formed from this population of size 5, disregarding order. Use the appropriate formula.

List all the samples of size 2 that can be formed from this population. Be sure the list is consistent with the answer obtained from the formula. Otherwise, check your work.

Calculate the mean of each of the samples of size 2.

Create a probability distribution of all the sample means from the sample of size 2. (HINT: If you have a mean of 7 in the list of sample means and it occurs 3 times out of 10, then the probability is 0.3 for that mean value.)

Calculate the mean and standard deviation of that probability distribution using the appropriate formulas.

[13 marks] A company is interested in forecasting demand for a product. They have reason to believe that the demand is not affected by any seasonal changes and that it does not increase or decrease systematically over time. They have data for the last 9 periods (below).

In each part of this question, show your work: show the equation you use, how you plug in, and your final answer. Please do not round any answers.

a) [3 marks] Use a 4-period moving average to forecast demand for period 10.

b) [3 marks] Use a 3-period weighted moving average to forecast demand for period 10 using weights of 0.6, 0.3, and 0.1, respectively. Show your work.

c) [3 marks] Suppose the forecast for period 9 was 235 units. Use exponential smoothing with a smoothing constant of 0.6 to forecast demand for period 10.

d) [4 marks] Suppose the actual demand in period 10 was 211 units. Which of your forecasting methods from parts a through c performed best, and why? Please provide a table and make your conclusion based on your table.

[13 marks] A company is interested in forecasting demand for a product. They have reason to believe that the demand is not affected by any seasonal changes and that it does not increase or decrease systematically over time. They have data for the last 9 periods (below).

In each part of this question, show your work: show the equation you use, how you plug in, and your final answer. Please do not round any answers.

a) [3 marks] Use a 4-period moving average to forecast demand for period 10.

b) [3 marks] Use a 3-period weighted moving average to forecast demand for period 10 using weights of 0.6, 0.3, and 0.1, respectively. Show your work.

c) [3 marks] Suppose the forecast for period 9 was 235 units. Use exponential smoothing with a smoothing constant of 0.6 to forecast demand for period 10.

d) [4 marks] Suppose the actual demand in period 10 was 211 units. Which of your forecasting methods from parts a through c performed best, and why? Please provide a table and make your conclusion based on your table.

Embassy Publishing Company received a six-chapter manuscript for a new college text- book. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the textbook will be successful. If successful, a profit of $600,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $200,000 will occur. Before making the decision to accept or reject the manuscript, the editor is consider- ing sending the manuscript out for review. The review cost $5000. A review process provides either a favorable (F) or unfavorable (U) evaluation of the manuscript. Past experience with the review process suggests that probabilities P(F) =0.7 and P(U)= 0.3 apply. Let s1 the textbook is successful, and s2 the textbook is unsuccessful. The editor’s initial probabilities of s1 and s2 will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows: P(s1 |F) =0.75   P(s1 |U)= 0.417      P(s2 |F)= 0.25                   P(s2 |U)= 0.583

a. Construct a decision tree assuming that the company will first make the decision of whether to send the manuscript out for review and then make the decision to accept or reject the manuscript.

b. Analyze the decision tree to determine the optimal decision strategy for the publish- ing company.

c. What is the expected value of perfect information? What does this EVPI suggest for the company?

Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.

a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)