代写MSIN0026、代写Java/c++编程

日期：2022-11-10 10:40

Product, Technology and Operations Management

Problem Set 1

This is an individual assignment, so no collaboration is permitted. Your submitted problem set

should contain:

A description of your solutions and calculation steps (do not just write the answers),

Your numerical answers as highlighted (by putting numbers in a rectangular box for

instance).

QUESTION 1 (20 POINTS)

The owner of a small manufacturing firm has patented a new device for washing dishes and

cleaning dirty kitchen sinks. Before trying to commercialize the device and add it to her existing

product line, she wants reasonable assurance of success. Variable cost is estimated as ￡8/unit

produced and sold, and a fixed cost per year is estimated to be ￡36,000.

(a) If the selling price is set at ￡18, how many units must be produced and sold to break

even?

(b) Forecasted sales for the first year are 5,000 units if the price is reduced to ￡16. What

would be the product’s total contribution to profits in the first year with this pricing

strategy?

QUESTION 2 (20 POINTS)

Consider the following simple assembly process:

Raw Material 6 min/unit 8 min/unit 3 min/unit Finished Goods

The numbers below each step refer to the time necessary to process one unit of the product at

that step.

The process is staffed by three operators with one operator assigned to each of the three steps.

Assume no set ups are required, processing times are constant, and no Work in Process (WIP) is

permitted beyond that actually being worked on at each process step (i.e., there are no buffers

between process steps).

(a) What is the Capacity of the process?

(b) What is the Capacity Utilization of the operator at Step A?

(c) Each operator receives regular wages of ￡12/hour for the first 8 hours, and overtime

wages of ￡18/hour for any additional time. The maximum work time permitted per day

is 12 hours. A finished unit sells for ￡14 while its direct material cost is ￡6/unit. Does it

pay to use overtime under this cost structure (assuming sufficient demand exists)?

(d) Would you hire a skilled operator whose wage rate were ￡25/hour (regular time), but

could perform Step B at a processing time of 4 minutes/unit?

(e) Same as (d), but performs Step A at a processing time of 2 minutes/unit?

QUESTION 3 (20 POINTS)

Consider the following batch flow process consisting of three process steps performed by three

machines:

Activity Time: 2 min/part 3 min/part 2.5 min/part

Setup Time: 20 min 0 0

Work is processed in batches at each step. Before a batch is processed at step 1, the machine

has to be set up. During a setup, the machine is unable to process any product.

(a) Assume that the batch size is 20 parts. What is the capacity of the process?

(b) For a batch size of 30 parts, which step is the bottleneck for the process?

(c) Using the current production batch size of 10 parts, how long would it take to produce

15 parts starting with an empty system? Assume that the units in the batch have to stay

together (no smaller transfer batches allowed) when transferred to step 2 and to step 3.

A unit can leave the system the moment it is completed at step 3. Assume step 1 needs

to be set up before the beginning of production.

(d) Using the current production batch size of 10 parts, how long would it take to produce

15 parts starting with an empty system? Assume that the units in the batch do not have

to stay together; specifically, units are transferred to the next step the moment they are

completed at any step. Assume step 1 needs to be set up before the beginning of

production.

QUESTION 4 (20 POINTS)

Tony Soprano sits at a table in the back of Corleone’s Grille and Pub waiting for visitors. If the

chair opposite Mr. Soprano is occupied, visitors wait at the bar. When the chair becomes free,

the next visitor sits down and talks to Mr. Soprano. Visitors arrive at a rate of 10 per hour, and

the arrival pattern follows an exponential distribution. Once seated, the visitor does not leave

until Mr. Soprano has finished the conversation. Mr. Soprano is quite unpredictable, and the

lengths of his conversations tend to follow an exponential distribution with a mean time of 5

minutes. Once the conversation is over, the visitor always leaves the restaurant.

(a) Each visitor has a taxi waiting outside. How much will each pay, on average, to keep the taxi

waiting while they are in the restaurant? Assume that a taxi charges ￡0.40 per minute to wait.

Recently, Tony’s business has picked up substantially, and his visitors have been arriving at the

restaurant at a rate of 30 per hour (again following an exponential distribution). Tony has found

that when his visitors wait at the bar, it costs him approximately ￡60 per hour per visitor since

the visitors all put drinks on his tab. To stem the increasing bar tab, Tony has decided to hire

assistants to hold conversations for him. Now, Tony no longer holds conversations. Rather, he

watches the assistants (who work considerably slower than he did) to ensure that each

maintains a mean conversation time of 6 minutes (exponentially distributed). Assume that

visitors at the bar go to whichever assistant is available first.

(b) If Tony can use four, five, or six assistants to hold his meetings, how many assistants should

he hire? Assume that each assistant gets paid ￡40 per hour, regardless of how busy they are.

Start by listing the costs that are relevant for your calculations.

QUESTION 5 (20 POINTS)

Write a brief summary of Dasher case study (300 words maximum). In your summary, make

sure you include the following in four bullet points:

Write a brief description of the case.

Which topic(s) from PTOM module are covered during the case study?

Write two things that you have learned from the case study.

In your opinion, what was the main message of the case study?