Problem Set 1 Spring 2024
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School
University of Maryland Global Campus (UMGC) *
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Course
105
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
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Uploaded by BrigadierDolphinPerson875
Problem Set 1
Use the information in the chart below corresponding to your assigned number to answer the five questions below. For questions 1,2,3,4 use columns A – C. For question 5 use columns D and E.
Show all your steps to reach each of your answers.
1.
You go to your favorite food market and see an item that you used to regularly purchase, although the last time was 8 months ago. The package looks the same
BUT looking at the label you see that the number of items in the package has decreased. What is the percentage of decrease in the quantity
from the original package to the new package? Round answer to one decimal place (ie the tenths). - Original Package: 30 items
- New Package: 20 items - The quality has changed by 30-20= 10 - The percentage of decrease in the quantity from the original package to the new package: (10/30)X 100%= 33.3%
2.
What should the price of the new package be to keep the original package quantity to cost ratio the same? Set up and solve a proportion to find this answer.
The original package costs $4.00 and had 30 items. The new package has 20 items.
To find the new price, we can set up a proportion:
(4/30)= (x/20)
Cross multiply and solve x:
x= (4x20)/30= $2.67
3.
Instead of a new lower price for the package with less items, the price is kept the
same as for the original package. This changes the unit price for each item. What is the percentage that the unit price
in the new package has increased from the unit price in original package? Round your answer to one decimal place.
Do NOT round when you find the unit prices. Only round your final percentage answer to one decimal place.
The original package had 30 items, and cost $4.00.
Ratio= 4/30=0.1333
The new package has 20, but also same cost
Ratio= 4/20= 0.2
The change in unit price will be: (4/20)- (4/30)= 0.0667
The percentage of increase is: (0.0667/0.1333)x 100% = 50%
4.
A store buys 125 cases of the new packages. Each case contains 15 packages. They take a 6-month simple interest installment loan at an annual interest rate of 2.3%. What will the monthly payment
be? Monthly payment= (Principal + Interest)/ Number of months
Price per package: $4.00
Total packages: 125 x 15= 1,875 Interest rate: 2.3%
Time: 6 months
Calculate principal amount: 1,875 x 4= $7,500
Calculate interest accrued over the loan term:
Interest= Principal x Interest Rate x Time = 7,500 x 0.023 x (6/12)
= $86.25
Monthly payment= (7,500 + 86.25)/ 6= $1,264.375
5.
Use the information in columns D and E to answer this question. As you are browsing the store you notice that the store is offering cookbooks. The sign by the product indicates the discount percentage and the resulting sale price. What was the original price
of the cookbook? Round to the nearest cents.
Original price= sale price/(1- discount rate)
Original price= 16.75/(1- 0.39)= $27.45
A use for questions 1-
4
B use for questions 1-
4
C use for questions 1-
4
D use for question 5
E use for question 5
Assigned
Number
Original Package: Number of items
New Package: Number of items
Price of original and new package
Percentage discount
Resulting Sale price
1
64 56 4.25
12%
12.50
2
30 25 6.00
22%
14.50
3
25 18 5.00
32%
16.50
4
15 10 6.50
13%
18.50
5
16 12 5.50
23%
20.50
6
64 52 7.00
33%
22.50
7
32 28 7.25
14%
24.50
8
300 260 7.50
24%
26.50
9
232 200 4.00
34%
28.50
10
40 34 4.50
15%
30.50
11
55 45 6.25
25%
12.00
12
35 25 4.75
35%
14.00
13
20 18 5.75
16%
16.00
14
10 7 6.75
26%
18.00
15
26 22 7.75
36%
20.00
16
54 42 4.25
17%
22.00
17
22 18 6.00
27%
24.00
18
200 160 5.00
37%
26.00
19
132 100 6.50
18%
28.00
20
50 44 5.50
28%
30.00
21
65 50 7.00
38%
10.75
22
30 20 7.25
19%
12.75
23
64 48 7.50
29%
14.75
24
30 20 4.00
39%
16.75
25
16 12 4.50
11%
18.75
26
64 48 6.25
21%
20.75
27
42 36 4.75
31%
22.75
28
400 360 5.75
13%
24.75
29
332 200 6.75
23%
26.75
30
60 48 7.75
33%
28.75
31
65 50 5.00
14%
30.75
32
30 15 6.50
24%
21.75
33
64 48 5.50
34%
25.75
34
40 30 4.75
15%
29.75
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35
150
100
3.00
25%
31.75
36
64
48
6.00
35%
33.75