The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad quality." The numbers of imperfections in different objects are independent of each other. A random sample set of seven objects is taken. What is the probability that the sample set has exactly two top quality, two good quality, two normal quality, and one bad quality objects?

Two pairs of siblings (two brothers and a brother/sister), and three only children (two men and one woman) sit in a row of seven consecutive seats. How many ways can they be seated:
i. with no restrictions;
ii. alternating genders;
iii. such that the women are all consecutive;
iv. such that twin siblings sit next to one another?

Birth certificates show that approximately 9% of all births in the United States are to teen mothers (ages 15 to 19), 24% to young-adult mothers (age 20 to 24), and the remaining 67% to adult mothers (age 25 to 44). An extensive survey of live births examined pregnancy type, defining an unintended pregnancy as one that was unwanted or mistimed by at least two years. The survey found that “only 23% of births to teen mothers are intended, and 77% are unintended. Among births to young-adult women age 20–24, 50% are intended, and at ages 25–44, 75% are intended.

Use your tree diagram and Bayes’s theorem to find the probability that a birth was to a teen mother if we know that the pregnancy was unintended.

(Spreadsheet Problem)

You run a manufacturing facility. Last year your facility manufactured 21 products with the following characteristics:

Activity-Based Costing (ABC)

In addition, the following data is known about last year:

- 1.1 million labor hours were used to build the 21 products (note, “labor hours” and “fabrication hours” are not the same)

- $37/hour labor rate

- Assume there is no inflation

You are considering manufacturing the following 3 new products:

Use ABC to determine how much you should quote customers for each of the products (assume no profit in the quotes). Your answer should be based on last year’s history (do not assume that products A, B, and C have or are necessarily going to be built)

Hints:

1)You will need to figure out the number of engineering hours and fabrication hours needed for the three new products

2)You can figure out the labor hours associated with each new product from last year’s ratio of labor hours to fabrication hours.

There is a deck with 42 cards, with 4, 5, 6, 7, 8, 9, A. There are three suits spades, hearts, and clovers. In each suit there are two of each card. So there are two 7 of spades, 7 of hearts, 7 of clovers and so on. Each hand dealt consists of 5 cards.

1. How many hands contains exactly a pair that consists of two cards with the same value?

2. How many hands contains exactly one pair with the same value but different suits?

3. How many hands contain exactly one 9 of spades?

Discrete Math.

Managers at Fluid Induction Industries are reviewing the economic feasibility of manufacturing a part that the company currently purchases from a supplier. Forecasted demand for this part is 16,800 units. Fluidoperates 250 days per year.

Fluid’s financial analysts established the cost of 9% for the use of funds for investments within the company. Also, over the past year $2,200,000 was the average investment in the company’s inventory. Accounting information shows that a total of $101,000 was spent on taxes and insurance related to the company’s inventory. Additionally, an estimated $29,000 was lost to inventory shrinkage, this included broken and damaged goods, and pilferage. $100,000 was spent on warehouse overhead, including expenses for heating and lighting.

Two hours are required to process and coordinate an order for the part regardless of the quantity ordered. Purchasing salaries average $28 per hour, including benefits. A detailed accounting analysis on 1,250 orders revealed that $25,000 was expensed for internet, paper and postage directly related to this ordering process.

Lead time for this part is one-week. The use of the part during the lead time is normally distributed with a mean of 960 units and a standard deviation of 16 units. The company’s policy regarding stock-outs is that one stock-out per year is permitted.

The company has a current contract to purchase the part from the supplier for $90 per unit. Fluid has increased its manufacturing capacity and is considering producing the part in house. The utilization of the increased capacity will produce at a rate of 4,800 units per month with up to 5 months of production time available. Management believes that with a two-week lead-time it can schedule the production of the part when needed. . The use of the part during the lead time is normally distributed with a mean of 1,280 units and a standard deviation of 200 units. Production costs are estimated at $76.50 per unit.

A major concern for the company is the fact that it will take two full 8 hour shift to set up the equipment. The total cost of labor is estimated to be $150 per hour.

Managerial Report.

Develop a managerial report that will address the question as to whether the company should purchase or manufacture the part itself. Include the following factors in your report:

1. An analysis of the holding cost.

2. An analysis of the ordering cost.

3. An analysis of setup cost.

4. Develop an inventory for ordering a quantity form the supplier and producing a quantity in house.

5. Include such information as Q, number of orders/production runs, cycle time, ROP, amount of safety stock, expected maximum inventory, annual cost of the units purchase or manufactured.

6. Make a recommendation to management whether the company should purchase or manufacture the part and the cost savings associated with your recommendation.

Suppose you are living on the planet Triskelion with your friends. If all birthdays are independent and all 88 days of Triskelion’s year are equally likely, what’s the probability that there is at least one birthday match among x people in a room? Graph this for x = 2, 3, . . . , 88. In particular, what does x have to be in order to assure at least a 50–50 chance of a match?

1. Suppose that a monopoly faces the demand, marginal revenue, and cost schedules below.

1. What quantity maximizes profit?
   
   The monopoly Q = ____
   
2. What price maximizes profit?
   
   The monopoly P = ____
   
3. What is the maximum profit?
   
   The maximum profit is $____________.
   
4. What is the socially efficient quantity?
   
   The socially efficient Q = _____

What is the deadweight loss when the monopoly produces the monopoly Q instead of the socially efficient Q?

The deadweight loss = $_______

Activity-Based Costing in a Service Organization

Banctronics Inc. has ten automatic teller machines (ATMs) spread throughout the city maintained by the

ATM Department. You have been assigned the task of determining the cost of operating each machine.

Management will use the information you develop, along with other information pertaining to the vol-

ume and type of transactions at each machine, to evaluate the desirability of continuing to operate each

machine and/or changing security arrangements for a particular machine.

The ATM Department consists of a total of six employees: a supervisor, a head cashier, two as-

sociate cashiers, and two maintenance personnel. The associate cashiers make between two and four

daily trips to each machine to collect and replenish cash and to replenish supplies, deposit tickets, and

so forth. Each machine contains a small computer that automatically summarizes and reports transac-

tions to the head cashier. The head cashier reconciles the activities of the two associate cashiers to the

computerized reports. The supervisor, who does not handle cash, reviews the reconciliation. When an

automatic teller’s computer, a customer, or a cashier reports a problem, the two maintenance employees

and one cashier are dispatched immediately. The cashier removes all cash and transaction records, and

the maintenance employees repair the machine.

Maintenance employees spend all of their time on maintenance-related activities. The associate

cashiers spend approximately 50 percent of their time on maintenance-related activities and 50 percent

on daily trips. The head cashier’s time is divided, with 75 percent directly related to daily trips to each

machine and 25 percent related to supervising cashiers on maintenance calls. The supervisor devotes

20 percent of the time to daily trips to each machine and 80 percent to the equal supervision of each

employee. Cost information for a recent month follows:

Salaries

Supervisor......................................................... $ 5,500

Head cashier....................................................... 4,000

Other ($2,100 each) ................................................. 8,400

Lease and operating costs

Cashiers’ service vehicle ............................................. 1,600

Maintenance service vehicle........................................... 1,500

Office rent and utilities ................................................. 4,000

Machine lease, space rent, and utilities ($1,700 each)......................... 17,000

Total ............................................................... $42,000

Related monthly activity information for this month follows:

Machine

Routine

Trips

Maintenance

Hours

1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 17

3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 15

4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 30

5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 15

6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 10

7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 25

8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5

9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 20

10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

18

Total ................................................. 500 160

Additional information follows:

• The of?ce is centrally located with about equal travel time to each machine.

• Maintenance hours include travel time.

• The cashiers’ service vehicle is used exclusively for routine visits.

• The of?ce space is divided equally between the supervisor and the head cashier.

Required

a. Determine the monthly operating costs of machines 7 and 8 when cost assignments are based on the

number of machines.

b. Determine the activity cost of a routine trip and a maintenance hour for the month given. Round

answers to the nearest cent.

c. Determine the operating costs assigned and reassigned to machines 7 and 8 when activity-based

costing is used.

d. How can ABC cost information be used by Banctronics Inc. to improve the overall management of

monthly operating costs?