The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows:

                       Warehouse

Plant           1                       2            Capacity

1                4                        7               450

2                8                         5              600

3                5                         6               380

                            Customer

Warehouse          1                        2                            3                             4

1                            6                       4                            8                             4

2                           3                         6                            7                             7

Demand                300                     300                         300                        400

Formulate the linear programming model to minimize the cost of shipping for this transshipment problem.

A-at the optimal solution how much is shipped from Plant 3 to Warehouse 1?

B-what is the range of optimality of coefficient of cost from Plant 3 to Warehouse 1 and what does this

mean?

C-what is the range of feasibility for the supply amount for Plant 2 and what does it mean?

D-what is the range of feasibility for the demand amount for customer 2 and what does it mean?

It is 2018. You decided to purchase a US treasury bond now. It matures in 8 years (in 2026), has a face value of $100,000, a coupon rate of 6 percent (as usually, you get the first coupon in a year, i.e. 2019) and a yield of 7 percent.

a) Even before proceeding to calculations, you refresh what you learnt in the M&B class and immediately realize that you would have to pay … rather than the face value of this bond. (choose: more or less)

b) Based on this information, you quickly calculate that you would have to pay $____ for this bond.

c) You purchased the bond back in 2017. It is 2018 now, and you’ve received the first coupon payment. Shortly after this, FED’s actions led to an unexpected change in yield of all bonds. The yield for your bond now is 9 percent. What is the price of your bond now?

d) but, if you actually feel completely indifferent to any changes in the bond price (even if it drops a lot) and yield, it must be the case that you planned originally to... (write a sentence or two explaining the reason when you feel not affected by this at all).

Problem 4-15 Contrasting ABC and Conventional Product Costs [LO4-2, LO4-3, LO4-4]

Marine, Inc., manufactures a product that is available in both a flexible and a rigid model. The company has made the rigid model for years; the flexible model was introduced several years ago to tap a new segment of the market. Since introduction of the flexible model, the company’s profits have steadily declined, and management has become concerned about the accuracy of its costing system. Sales of the flexible model have been increasing rapidly.

Overhead is applied to products on the basis of direct labor-hours. At the beginning of the current year, management estimated that $418,500 in overhead costs would be incurred and the company would produce and sell 1,000 units of the flexible model and 11,500 units of the regular model. The flexible model requires 2.0 hours of direct labor time per unit, and the regular model requires 1.00 hours. Direct materials and labor costs per unit are given below:

Required:   

1-a. Compute the predetermined overhead rate using direct labor-hours as the basis for allocating overhead costs to products.

1-b. Compute the unit product cost for one unit of each model.

2. An intern suggested that the company use activity-based costing to cost its products. A team was formed to investigate this idea. It came back with the recommendation that four activity cost pools be used. These cost pools and their associated activities are listed as follows:

Compute the activity rate for each of the activity cost pools.     

3-a. Using activity-based costing, determine the total amount of overhead that would be assigned to each model for the year.

3-b. Using activity-based costing, compute the unit product cost for one unit of each model.

f(x) = 15x^4-3x^5 / 256. f'(x) = 60x^3 - 15x^4 / 256 f''(x) = 45x^2 - 15x^3 / 64

Find the horizontal and vertical asymptotes

Find the local minimum and maximum points of f(x)

Find all inflection points of f(x)

Minimize ?(?,?)=3?−2?+6f(x,y)=3y−2x+6 subject to ?≥−3,    ?≤4,    4?+7?≤23,    8?+7?≥−31.

Solve the following linear programming problem using the dual simplex method:

max ? = −?1 − 2?2

s.t.

−2?1 + 7?2 ≤ 6

−3?1 + ?2 ≤ −1

9?1 − 4?2 ≤ 6

?1 − ?2 ≤ 1

7?1 − 3?2 ≤ 6

−5?1 + 2?2 ≤ −3

?1,?2 ≥ 0

Dream Team Productions is in the final design phases of the new film, Killer Worms, to be released next summer. Market Wise, the firm hired to coordinate the release of the Killer Wormstoys, identified the following activities to be completed before the release of the film.

Activity           Immediate        Optimistic       Most likely      Pessimistic      Normal Crash Crash   

                        Predecessor     Time (weeks)  Time(weeks)   Time(weeks)   Cost       Cost   time

A                     ----                   1                      2                                  4          1000       1900   1

B                     ----                   3                      3.5                               4          1000       1800   2

C                     A,B                 10                    12                                13        1500        2700  8

D                     C                     4                      5                                  7          2000        3200  4

E                      C                     2                      4                                  5          5000        8000  3

F                      E                      6                      7                                  8          3000        4100  6

G                     C                     2                      4                                  5.5       8000        5000  2

H                     D,F,G              5                      7.7                               9          5000        6400  7

I                       D,F                  9.9                   10                                12        10000        ----- -

J                      H                     2                      4                                  5          4000          ----- -

K                     I,J                    2                      4                                  6          5000          ----- -

- - 1). Determine a crashing schedule.

You work for a Realtor agency and part of the agency's job is to advise clients on the asking price. Based on your experience you know that buyers tend to focus on the size of the house, the number of bedrooms, number of bathrooms, and the age of house. You take a sample from the hundreds of houses that the agency sold over the past six months and plan to run a regression analysis in order to find out which variables significantly impact price and how.

(1) State the null and alternative hypothesis for each independent variable.

(2) Explain how you expect each independent variable to impact the dependent variable.

(3) Conduct regression analysis, find the final model in which only significant IVs remain.

(4) Recommend an asking price for a client whose house is 1800 squared feet, has 3 bedrooms, 2 bathrooms, and was constructed in 1980.

Abstract Algebra

Let n ≥ 2. Show that S_n is generated by each of the following sets.

(a) S₁ = {(1, 2), (1, 2, 3), (1, 2, 3, 4), ..., (1, 2, 3,..., n)}

(b) S₂ = {(1, 2, 3, ..., n-1), (1, 2, 3, ..., n)}

A consulting company was tasked with identifying which market segment would be more profitable, labeled as Segment A or Segment B. A survey was created showing a product to the two different segments, and respondents were asked to rate the product on a scale from 1 to 10 (1 worst, 10 best). Use data from "segment" sheet.

Which of the following are correct? More than one answer is possible.