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?

1) High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.3. A sample of 81 U.S. adults is chosen.

a) What is the sampling distribution of?

pˆ

b) Find the probability that the proportion of individuals in the sample who have high blood pressure is between 0.24 and 0.35.

c) Find the probability that less than 26% of the people in the sample have high blood pressure.

d) Find the probability that more than 28% of the people in the sample have high blood pressure.

e) Would it be unusual if more than 31% of the individuals in the sample of 81 had high blood pressure? Explain.

2) Researchers obtained the body temperature of 93 healthy humans and found the average body temperature of these 93 people to be 97.3°F. Construct a 99% confidence interval for the population mean body temperature of healthy humans. Assume σ = 0.63°F. Interpret your result.

3) A firm would like to estimate the mean age of all people in the civilian labor force. What size sample would be required to estimate the mean age of all people in the civilian labor force accurate to within 0.75 year of the estimate at the 95% confidence level, given that σ = 15.26 years?

4) The average monthly electric bill of a random sample of 35 residents of a city is $90 with a standard deviation of $24. Construct a 98% confidence interval for the population monthly electric bills of all residents. Interpret your result.

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 8.20%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 25.07%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?  

   1. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   4. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.