4. Consider the random variable Z from problem 1, and the random variable X from problem 2.

Also let f(X,Z)represent the joint probability distribution of X and Z.  f is defined as follows:

f(1,-2) = 1/6
f(2,-2) = 2/15
f(3,-2) = 0
f(4,-2) = 0
f(5,-2) = 0
f(6,-2) = 0
f(1,3) = 0
f(2,3) = 1/30
f(3,3) = 1/6
f(4,3) = 0
f(5,3) = 0
f(6,3) = 0
f(1,5) = 0
f(2,5) = 0
f(3,5) = 0
f(4,5) = 1/6
f(5,5) = 1/6
f(6,5) = 1/6

Compute the covariance of X and Z.

Then, compute the correlation coefficient of X and Z. (Note: You will need values that you computed in problems 1 and 2.)

These are questions 1 and 2.

1. Let Z be a random variable with the following probability distribution f:

f(-2) = 0.3
f(3) = 0.2
f(5) = 0.5

Compute the E(Z), Var(Z) and the standard deviation of Z.

2. Tossing a fair die is an experiment that can result in any integer number from 1 to 6 with equal probabilities. Let X be the number of dots on the top face of a die. Compute E(X) and Var(X).

Ginny is endowed with $10 million and is deciding whether to invest in a restaurant. Assume perfect capital markets with an interest rate of 6%.

2. Which investment option should Ginny choose?

Ginny is actively pursuing another business venture as a ticket scalper. She estimates that for a $2 million investment in inventory she can resell her tickets for $6 million over the next year (cash flows realized in exactly one year).  Assume the same 6% interest rate.

3. What is the NPV of the Ticket Brokering venture?
4. What is the new value of Ginny’s Corporation?
5. Suppose Ginny does not want to use her own $2 million to start the new venture. Instead, she wants to raise equity capital by issuing 100,000 new shares. What price will new investors be willing to pay?
6. How many shares will need to be sold to outside investors?
7. How will your answer differ if Ginny is not guaranteed to resell the tickets for $6 million?
8. According to Ginny’s prospectus, cash flows from ticket sales (net of expenses) are expected to follow the following distribution:

What is the new value of Ginny’s Corporation?

9. What price will new investors be willing to pay for Ginny’s shares?

Please only answer Q6, Q7, Q8, Q9 four questions. Thanks.

A kitchen appliance manufacturer is deciding whether or not to introduce a new product. Management has identified three possible demand regimes, with associated projected income for the first year of operation. In addition, if the company decides to produce the new product, it can do so by using its existing facilities, which will cost it $3,500,000 in renovations; or build a new facility, which will cost $6,500,000. Expanding will allow it to make more product and so its potential sales can be higher. The following table contains a summary of management expectations:

The company believes that if the new product is not introduced, in the first year of operation the company will lose $10,500,000 in sales to competitors in a high demand regime, $1,500,000 in a medium demand regime, and $0 in a low demand regime.

(a) Construct a payoff table and decision tree for this problem.

(b) Using the expected value approach, what should the company do?

(c) The company finds itself in a difficult financial situation. How does this information affect your recommendation in part (b)?

(d) A consulting company claims it can perform a more thorough market research study. In your opinion, should this study be performed?

(e) The company has the option of constructing a new facility after 1 year of operation. In your opinion, which conditions would warrant an expansion after year 1?

The following data are for the two products produced by Shakti Company.

The company's direct labor rate is $20 per direct labor hour (DLH). Additional information follows.

I am getting stuck on the following:

4.1 How Much gross profit is generated by each customer of Product A and Product B.

Gross profit (loss) per unit Product A $5.71 Product B $24.98

Units purchased per customer 20 5

Gross Profit (loss) per customer ? ?

4.2 Is the gross profit adequate for each customer of Product A and Product B?

Gross profit (loss) per customer Product A ? Product B ?

Service Cost Per Customer 90 90

Profit (loss) per customer ? ?

Problem 7-41

Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.

1. Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. If required, round your answers to two decimal places.
   

   Let R	=	number of gallons of regular gasoline produced
   P	=	number of gallons of premium gasoline produced

   Max	R	+	P
   s.t.
   	R	+	P	≤		Grade A crude oil available
   	R	+	P	≤		Production capacity
   			P	≤		Demand for premium
   			R, P	≥

2. What is the optimal solution?
   

   Gallons of regular gasoline
   Gallons of premium gasoline
   Total profit contribution	$

3. What are the values and interpretations of the slack variables?
   

   Constraint	Value of Slack Variable	Interpretation
   1
   2
   3

4. What are the binding constraints?
   

   Grade A crude oil available
   Production capacity
   Demand for premium

You need to validate the concentration of a 50 μL stock solution reported it be 25 mg/mL based single measurement. To conserve sample you decide to use the UV-vis plate reader to make an absorbance measurement using a 100 μL well-volume.

Given:

The protein has a molecular weight of 6,343 g/mol. and a molar extinction coefficient or 113,268 M-1cm-1 (Effective pathlength = 0.3 cm for a 100 μL well volume). The instrument you have available provides accurate absorbance readings for sample absorbance in the range 0.1 - 1. 0. You have P20 and P200 pipettes and 20 mM phosphate buffer available.

a) What fold dilution of the sample would be needed get and absorbance of 0.5?

b) Describe how you dilute 2 μL of the 25 mg/mL sample so that this absorbance reading can be made.

c) After completing a single measurement of the sample your calculations indicate the sample is 26.7 mg/mL. What percent agreement exists between your determination and the previously reported value? What factors are most likely?

d) You need to assay the purity of the sample from parts A-C by SDS-PAGE. Explain how to prepare a 20 μL sample containing 30 μg for this experiment.

After combining with 2x sample loading buffer and heating, you transfer 25 μL of the denatured protein into a well of the resolving gel.

Compute the total amount of protein that was added to the gel in micrograms and nanomoles.

QUESTION 4

1. Company ABC is a manufacturing company specialized in three auto parts denoted by X, Y, and Z respectively. The company is preparing for the budgets for the next year and has collected the following information:

1. The company allocates $10 of variable overhead cost to each labor hour.
2. The total fixed cost for the entire company is $300,000.
3. The company has a total labor budget of $50,000 with an hourly labor cost of $10.
4. After calculation, it costs $0.5 to run the machine for 1 hour. Company’s total budget for running machine is $20,000.

Required: (Please note that you should answer the questions in Word offline and please do NOT answer in the Blackboard!!!)

5. Does the company have any constraint? If yes, what is the constraint?
6. Given the constraint, what is the optimal production plan for the company that maximizes the company’s profit?
7. Company ABC has another two products: A and B. A can be sold “as is” (price: $300) or processed further into product A1 (price: $500). B can be sold “as is” (price: $200) or processed further into product B1 (price: $280). The allocated joint costs of A and B are $20 and $10, respectively. The cost of further processing costs of A and B are $185 and $78, respectively. Which product should be processed further and why?

Question 1) As water passes from a pipe of larger diameter to a pipe of smaller diameter in converging section, the static pressure:

Becomes half

Increases

Decreases

Does not change

Question 2) The following reading have to be recorded from the flow measurement apparatus to calculate the mass flow rate from the venturimeter?

Pressures at the inlet and exit of the venturimeter

Pressures at the inlet and throat of the venturimeter

The rotameter reading venturimeter

The pressure at the throat and exit of the venturimeter

Question 3) If the flow rate of water increases, then the pressure drop in the venturimeter

increases

decreases

remains same

cannot say

Question 4) The pressure measuring instrument can directly provide electrical signals which could be used to collect data using data acquisition systems and read on a PC

Bourdon Gauge

inclined manometer

Pressure Transducer

Vertical manometer

Question 5) How do you vary the flow rate through the fluid fow measurement experimental setup?

by increasing or decreasing the amount of water coliected in the weighing tank

by increasing or decreasing the time taken to collect the amount of water in the weighing tank

by varying the speed of the pump

by closing or opening the valve at the discharge section of the apparatus

Question 6) In the flow measurement experiment, consider using the weighing tank method for measuring the flowrate. If a 6 kg mass is added to the weight hanger and it takes 60 seconds for the weight hanger to move up again, how much will be the calculated flow rate? (show steps please)

1 kg/s

3 kg/s

0.3 kg/s

0.1 kg/s

A certain compound, A, reacts to form products according to the reaction A → P. The amount of A is measured as a function of time under a variety of different conditions and the tabulated results are shown here:

Make a graph of [A] vs. t, a graph of ln[A] vs. t, and a graph of 1/[A] vs. t using the data for 25 °C. Then make similar graphs for the other temperatures. What is the order of the reaction with respect to A? Explain your answer.

a. Use the data to determine the rate constant at each temperature. b. What is the activation energy for this reaction?

c. The same reaction is conducted in the presence of a catalyst, and the following data are obtained:

What effect does a catalyst have on the rate of the reaction? What is the activation energy for this reaction in the presence of the catalyst? How does it compare with the activation energy for the reaction when the catalyst isn’t present?