math;decision support

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uvpxf2004

Mathematics

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Decision support, excel Please see questions that are attached and please show work. Thank you for your help

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Problem 1 The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus State football game on Saturday. The ticket seller can serve an average of 12 customers per hour; on average, 10 customers arrive to purchase tickets each hour (Poisson distributed). Determine the average time a ticket buyer must wait and the portion of time the ticket seller is busy. Problem 2 The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 7.5 minutes, on aver- age. The machine operator can process an average of 10 parts per hour. Determine the average number of parts waiting to be worked on, the percentage of time the operator is working, and the percentage of time the machine is idle. Problem 3 The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway. Planes arrive at the airport at the rate of 4 per hour. a. Determine the average number of planes that will stack up, waiting to land. b. Find the average time a plane must wait in line before it can land. c. Calculate the average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land. d. The FAA has a rule that an air traffic controller can, on average, land planes a maximum of 45 minutes out of every hour. There must be 15 minutes of idle time available to relieve the tension. Will this airport have to hire an extra air traffic controller? Problem 4. During registration at State University every semester, students in the college of business must have their courses approved by the college adviser. It takes the adviser an average of 2 minutes to approve each schedule, and students arrive at the adviser’s office at the rate of 28 per hour. a. Compute L, Lq, W, Wq, and U. b. The dean of the college has received a number of complaints from students about the length of time they must wait to have their schedules approved. The dean feels that waiting 10.00 minutes to get a schedule approved is not unreasonable. Each assistant the dean assigns to the adviser’s office will reduce the average time required to approve a schedule by 0.25 minute, down to a minimum time of 1.00 minute to approve a schedule. How many assistants should the dean assign to the adviser? Problem 5 Hayes Electronics in Problem 1 assumed with certainty that the ordering cost is $450 per order and the inventory carrying cost is $170 per unit per year. However, the inventory model parameters are frequently only estimates that are subject to some degree of uncertainty. Consider four cases of variation in the model parameters: (a) Both ordering cost and carrying cost are 10% less than originally estimated, (b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is 10% higher and carrying cost is 10% lower than originally estimated, and (d) ordering cost is 10% lower and carrying cost is 10% higher than originally estimated. Determine the optimal order quantity and total inventory cost for each of the four cases. Prepare a table with values from all four cases and compare the sensitivity of the model solution to changes in parameter values. Problem 6 The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 35,000 yards of denim per year to make jeans. The cost of ordering denim from the textile company is $500 per order. It costs Western $0.35 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.
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Explanation & Answer

hey buddy, please find attached the solution to your assignment.

Running Head: DECISION SUPPORT ASSIGNMENT

Decision Support Assignment
Name
Instructor
Course
Date

1

DECISION SUPPORT ASSIGNMENT

2
Problem 1

Average time a ticket buyer must wait:
λ = 10⁄hour
μ = 12⁄hour
Wq = λ⁄μ(μ − λ) = 10⁄12(12 − 10) = 0.417 hours = 25 minutes
𝐖𝐪 = 𝟐𝟓 𝐦𝐢𝐧𝐮𝐭𝐞𝐬
The portion of time the ticket seller is busy:
p = λ⁄μ = 12 = 0.833hours = 50 minutes.
10

𝐩 = 𝟓𝟎 𝐦𝐢𝐧𝐮𝐭𝐞𝐬
Problem 2
Average number of parts waiting to be worked on:
λ = mean number of part arrivals per hour = 60⁄7.5 = 8 parts per hour.
μ = mean service rate = 10 parts⁄hour
L = λ⁄(μ − λ) = (10−8) = 4 parts
8

𝐋 = 𝟒 𝐩𝐚𝐫𝐭𝐬
The percentage of time the operator is working:

DECISION SUPPORT ASSIGNMENT

3

p = λ⁄μ = 10 = 0.8 = 80%
8

𝐩 = 𝟖𝟎%
The percentage of time the machine is idle:
I = 1 − p = 1 − 0.8 = 0.2 = 20%
𝐈 = 𝟐𝟎%
Problem 3
λ = 4 airplanes per hour
μ = 60⁄12 = 5 per hour
a) Lq = λ2 ⁄μ(μ − λ) = 42 ⁄5(5 − 4) = 3.2
𝐋𝐪 = 𝟑. 𝟐
b) Wq = λ⁄μ(μ − λ) = 4⁄5(5 − 4) = 0.8 hours = 48 minutes
𝐖𝐪 = 𝟒𝟖 𝐦𝐢𝐧𝐮𝐭𝐞𝐬
1
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Anonymous
This is great! Exactly what I wanted.

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