# Path components

(See attached file for full problem description with proper symbols and equations)

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Let X be a topological space. Mapping a point to the path component which contains x establishes a map .

Show that for any continuous map between topological spaces, there exists a map such that the following holds:

?

? for two continuous maps and we have

? for the identity we have where the latter map denotes the identity on .

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https://brainmass.com/math/algebraic-geometry/path-components-55188

#### Solution Preview

Please see the attachment.

Proof:

Look at the above figure. Since is a continuous map, then maps a path connected component to a path connected ...

#### Solution Summary

This solution is comprised of a detailed explanation to show that for any continuous map between topological spaces, there exists a map such that the following holds:

?

? for two continuous maps and we have

? for the identity we have where the latter map denotes the identity on .

What is the average waiting time spent by a customer in the system? What is the average time a customer has to wait before he/she is serve? What is the average number of customers in the queue? What is the EOQ for this component? What is the cycle time in months? Draw the network and label. Designate normal & Crash critical paths.Smulate 10 hours of car arrivals and compute the average number of arrivals per hour.

1. The Town Bank's management is very concerned about customer service and has hired you to do a study on their current service. You find the following;

Customer arrive at an average of 35 per hour through the day except between 12 and 1 p.m. when it increases to one every minute. There are 4 teller windows and it takes on average 4 minutes to service a customer. During rush hour (i.e. from 12 to 1 p.m.) an additional teller window is opened to reduce waiting time.

(a) What is the average waiting time spent by a customer in the system

(1) During normal hours?

(2) During rush hour?

(b) What is the average time a customer has to wait before he/she is serve

(1) during normal hours

(2) during rush hour?

(c) What is the average number of customers in the queue

(1) during normal hours?

(2) during rush hours?

(d) What is the probability that a customer does not have to wait

(1) during normal hours?

(2) during rush hours?

(e) If the bank manager wishes to keep average waiting time down to three minutes, should be open additional windows and how many

(1) during normal hours?

(2) during rush hours?

4. The XYZ Company purchases a component used in the manufacturing of automobile generators directly from the supplier. XYZ's generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year. If ordering costs are $25.00 per order, Unit cost is $3.50 per component, and annual inventory holding costs are charged at 20%, answer the following inventory policy questions for XYZ:

(a) What is the EOQ for this component

(b) what is the cycle time in months?

(c) what are the total annual inventory holding and ordering costs associated with your recommended EOQ?

(d) Assuming 250 days of operating per year and a lead time of 10days, what is the reorder point for the XYZ Company?

(e) Suppose that XYZ's management like the operational efficiency of ordering in quantities of 500 units and ordering every two weeks. How much more expensive would this policy be than your EOQ recommendation?

(f) Would you recommend favor of the 500-unit order quantity? Explain.

(g) what would the reorder point be if the 500 unit quantity were acceptable?

Suppose the XYZ company decided to operate with a backorder inventory policy. Backorder costs are estimated to be $10 per unit per year. Find the following:

(h) minimum cost order quantity.

(i) Maximum number of backorders.

(j) cycle time.

(k) total cost including a breakdown of backorder costs, holding cost, and ordering cost.

5. XYZ builderws manufactures steel storage sheds for commercial use. The president is contemplating producing sheds for home use. The activities necessary to build an experimental model and related data are given in the accompanying table.

(see attached file)

(a) Draw the network and label.

(b) Designated normal & Crash critical paths.

(c) Crash to the limit and determine optimum cost.

(d) If you were given a budget of $13,600, how far can one crash?

7. The number of cars arriving at Lundberg's Car Wash during a given period of operation is observed to be the following:

No. of cars

Arriving Frequency

3 or less 0

4 20

5 30

6 50

7 60

8 40

(a) Simulate 10 hours of car arrivals and compute the average number of arrivals per hour. Use the random numbers that follow: 44, 49, 57, 97, 48, 63, 18, 10, 16, 70.

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