Two tanks each contain 100 gal of water and tank 2 initially has 50 lbs of salt uniformly dissolved in it. An external flow brings adds 5 gal/min to tank 1 with 5 lbs of salt in it. Tank 1 feeds tank 2 at 10 gal/min, and tank 2 feeds back to tank 1 at 5 gal/min. Finally, an exit stream leaves tank 2 at 5 gal/min.

1) Use Laplace transforms to solve the system of ODEs modeling this system and report the amount of salt in tank 2 as a function of time.

2)find the Homogeneous solution for the system of ODEs above without Laplace transforms; instead, using eigenvalues/eigenvectors.

3)Solve the Particular solution for the system of ODEs above using Undetermined Coefficients.

Consider a stock which is currently selling for $50. Construct a two-step binomial tree, 1-month and 2-months respectively for each of the two steps. The stock market volatility is 30%, the rate of interest is assumed to be 5% and the exercise price is $52.

(i) Calculate the price of an American Put.

(ii) Provide a graphical illustration to demonstrate how the put price and the put payoff change with respect to changes in the stock price.

(iii) Put all in an excel format

Consider a stock which is currently selling for $50. Construct a two-step binomial tree, 1-month and 2-months respectively for each of the two steps. The stock market volatility is 30%, the rate of interest is assumed to be 5% and the exercise price is $52. (i) Calculate the price of an American Put. (ii) Provide a graphical illustration to demonstrate how the put price and the put payoff change with respect to changes in the stock price. (iii) Put all in an excel attachment or copy and paste entire excel sheet

A reversible heat engine operates between two reservoirs at temperatures

700

°C

푎푛푑

50

°C

.

The engine drives a reversible refrigerator which operates between reservoirs at temperatures

of

50

°C

푎푛푑

−

25

°C

. The heat transfer to the engine is 2500 KJ and the net work output of the

combined engine refrigerator plant is 400 KJ.

i)

Determine the heat transfer to the refrigerant and the net heat transfer to the reservoir

at

50

°C

ii)

Reconsider (i) above given that the efficiency of the heat engine and the COP of

the refrigerator are each 45%

of their maximum possible values

4-9. Describe two ways how a firm can determine from a list of 50 to 100 internal factors the 20 most important factors to include in an IFE Matrix

Question 1

What post-translational modification will cause the biggest increase in the size of a protein, immediately when added?

Select one:

a. Phosphorylation

b. Ubiquitination

c. Acetylation

d. Methylation

Question 2

What does HMT do?

Select one:

a. It acts as an epigenator

b. It modifies nitrogenous bases

c. It produces euchromatin

d. It modifies histones

Question 3

Where can an epigenetic maintainer act?

Select one:

a. On the sequence of nucleotides

b. On the sequence of nucleotides and on the nucleotides directly

c. On certain nucleotides and amino acids

d. On certain amino acids

e. On certain nucleotides

Question 4

Which of the following types of protein could be coded by a tumour-suppressor gene?

Select one:

a. A protein that stimulate progression through the cell cycle.

b. A protein that forms part of a growth factor signaling pathway.

c. A protein that codes for a DNA repair enzyme.

d. A protein that helps prevent apoptosis.

e. A protein that repairs lost telomeres

Question 5

Which is NOT a typical mechanism by which a proto-oncogene is converted to an oncogene?

Select one:

a. A point mutation in the proto-oncogene

b. A chromosomal translocation resulting in the up-regulation of the proto-oncogene

c. Duplication of a chromosome region containing a proto-oncogene

d. Complete deletion of the proto-oncogene

e. Amplification of the proto-oncogene

Question 6

Why do you think familial retinoblastoma and Li-Fraumeni are considered to be inherited as autosomal dominant traits when the responsible genes are recessive?

Select one:

a. They are expressed in a dominant fashion in males, but recessive in females.       

b. People with this mutation are always homozygous for this allele.

c. If you are born with one allele mutated in every cell, the chance that the other allele will be mutated in one of the retinal cells is extremely high.

d. This recessive gene needs only one copy to express this phenotype.

e. Retinoblastoma was mischaracterized originally when it was called an autosomal dominant trait.

Question 7

Question text

In a normal cell, pRB binds to __________, which inhibits cell division. In the presence of __________ pRB becomes __________, which leads to cell division.

Select one:

a. cyclin+Cdk; oncogenes; dephosphorylated

b. transcription factors; cyclin+Cdk; phosphorylated

c. tumor suppressor; p53; phosphorylated

d. p21; p53; dephosphorylated

e. tumor suppressor; p21; hyperactive

Question 8

The following information relates to the next three questions:

A few decades ago, Knudsen and colleagues proposed a theory that, for a normal cell to become a cancer cell, a minimum of two genetic changes had to occur in that cell. Knudsen was studying retinoblastoma, a childhood cancer of the eye.

Two children are born from the same parents. Child one inherits a predisposition to retinoblastoma (one of the mutations) and child two does not. However, both children develop the retinoblastoma. Which of the following would you expect?

Select one:

a. a history of exposure to mutagens in child one but not in child two

b. increased levels of apoptosis in both children

c. an earlier age of onset in child one

d. decreased levels of DNA repair in child one

e. a more severe cancer in child one

Question 9

In colorectal cancer, several genes must be mutated in order to make a cell a cancer cell, supporting Knudsen’s hypothesis. Which of the following kinds of genes would you expect to be mutated?

Select one:

a. genes that are especially susceptible to mutation

b. the same genes that Knudsen identified as associated with retinoblastoma

c. genes coding for enzymes that act in the colon

d. the genes of the bacteria that are abundant in the colon

e. genes encoding transcription factors that regulate cyclin production

Question 10

Knudsen and colleagues also noted that persons with hereditary retinoblastoma that had been treated successfully lived on but then had a higher frequency of developing osteosarcomas (bone cancers) later in life. This provided further evidence of their theory because:

Select one:

a. osteosarcoma cells express the same genes as retinal cells.

b. one of the mutations involved in retinoblastoma is also one of the changes involved in osteosarcoma.

c. p53 gene mutations are common to both tumours.

d. retinoblastoma is a prerequisite for the formation of osteosarcoma later in life.

e. both kinds of cancer involve uncontrolled proliferation of cells.

1. Bradford Company has two service departments, Human Resources and Janitorial, and two production departments, Cutting and Glazing. The following data have been estimated for next year’s operations:

Requirements:

(1)   Distribute the service department costs using the sequential distribution method. Distribute the Human Resources Department first. (24 points/3 points each)

(2) Prepare the journal entries to distribute the costs of the service departments to the production departments given the results of your calculations. (16 points/8 points each)

ANS:

(1)      Sequential Distribution Method:

(2)

Brutus Auto is a thriving, independently owned and operated firm located in Westerville. It was founded in 1986 by “Brutus” Cooper. Brutus was born and raised in Westerville, OH. Brutus is well-known and trusted by the residents of the town. As a teenager, he was a star football player for the high school team. In his spare time, he enjoyed working on cars and had a special talent when it came to cars. After college, this hobby led Brutus to start his own business – Brutus Auto Tire and Lube.

Brutus does a wide variety of work on vehicles of all makes and models. The shop also offers a variety of parts and supplies at retail. Brutus spends a great deal of time conversing with customers, most of whom he has known his whole life. His reputation for honest and reliable work has earned him many repeat customers, with the positive word of mouth helping him to expand his business.

His wife, Diane, runs the office, and takes special care to acknowledge customers on their birthdays with hand-written cards that include coupons for discounted services. Customers often reflect that Brutus offers the kind of service you can only find from a small-town mechanic. While Brutus is slightly more expensive than the chain establishments that have recently moved into town, customers testify that the friendly environment and quality service are worth the price.

Operational details

Brutus’s shop has grown steadily over the years. Originally, Brutus maintained a modest three automobile bays at his shop, and he and his long-time buddy, Fred, conducted most of the work except oil changes which were handled by a part-time apprentice. Currently, Brutus shop has six bays (the layout of the shop is shown in Figure 1) and seven mechanics (as not all of the service activities require a bay). Each of the bays is identical so that any employee can work at any station.

Four of the employees (including Brutus and Fred) are full-time (work at least 40 hours per week), and three are interns who work part-time (work fewer than 40 hours per week). Brutus and Fred are the only two mechanics permitted to do work beyond the basics, and so more involved car services can take some time getting through the shop. Most mechanics at Brutus Auto were trained at the area vocational school, and those with particular skill are taken on as apprentices who work under Fred and Brutus on the more involved projects. Cooper provides all the tooling necessary, and is respected as a fair and caring boss. In return, Brutus’ employees are loyal and hard-workers; seldom is absenteeism a problem, and turnover is rare.

The employee schedule for a typical week is shown in Table 1. The numbers shown in Table 1 are all devoted to working on vehicles. The shop closes for one week in the winter.

Inventory

Although the shop is primarily a service provider, all of the services require materials in addition to labor, and so there are inventory considerations that Brutus must manage.

A variety of other parts and supplies (for example, oil filters and oil) must be kept available due to the regularity of use; it would be difficult to meet the high expectations of customers if these items are not available. This has become a particularly high priority ever since national service chains moved into town, as the speed of their services such as oil changes is already far superior to that of Brutus. As a result of these competitive pressures, Brutus sets a 98% target service level.

Brutus is dedicated to using a high-quality brand of parts and supplies, most of which are available from a single supplier. Note that these parts and supplies are not only used to support services but also sold as retail transactions to customers who wish to perform their own repair work.

Currently, a continuous review policy is used for all car parts and supplies, but Brutus believes this system may require too much time to maintain for all inventory items. A sample of some of the items offered, the volumes used in services and sold at retail, and the associated costs are shown in Table 2. Brutus has determined that to call the supplier, pay for transportation, and put a shipment away costs approximately $50. The stockroom is relatively small and does not require special equipment or personnel. There is virtually no theft of product, so the annual holding costs are approximately 25% of unit cost. Delivery of orders takes about one week from the local supplier.

Adding Tire Service

The owners believe that adding tire replacement would increase revenues with a negligible increase to fixed (facility) costs other than tire inventory. However, in order to be competitive with the discount chains, Brutus must target a maximum of 30 minutes total time for each customer visit specific to tires since pricing was already competitive. They estimate that the time between arrivals for cars needing such replacement would be ten minutes. A dedicated and secure parking lot with a limit of 6 spots is available specifically for cars awaiting tire service. While service requirements vary, they estimate that a dedicated technician should finish up 3 tire service jobs each hour.

1. - Identify and describe TWO recommendations you would make to

                           Brutus Cooper to improve Operations and/or to lower costs.