HW 3_Solved (1)
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Northwest Mississippi Community College *
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Course
530
Subject
Industrial Engineering
Date
Apr 3, 2024
Type
docx
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Uploaded by zzylla15
SCMS 3711: HW 3
Assigned: March 23, 2023
Due: Electronically via Canvas by March 30, 2023.
Rules for submitting HW 3:
1.
Please work with your group 2.
Your HW submission should contain one Excel file (Use different tabs for different questions and name them appropriately
) and one word file (you may edit this file).
3.
Please save your files in the following format: HW3_Your Group Name (example: If I were to submit my homework and I belonged to Group 1, I would name the file as HW3_Group1.)
4.
Please include the names of your group members and group name in your word document. Homework 3
Group Number:
Name
Contributions
Group member 1:
Group member 2:
Group member 3:
Part I – Component Manufacturing (3 points)
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components
are processed on two machines: a shaper and a grinder. The times (in minutes) required on each
machine are as follows:
Component
Shaper
Grinder
1
5
4
2
8
5
3
4
2
The shaper is available for 120 hours, and the grinder for 110 hours. No more than 200 units of
component 3 can be sold, but up to 1,000 units of each of the other components can be sold. In fact, the
1
company already has orders for 600 units of component 1 that must be satisfied. The per unit profit (in
dollars) for each of the three components are as follows:
Component
Profit Margin
1
8
2
6
3
9
a.
Formulate and solve for the recommended production quantities that will maximize
contribution to profit. In other words, determine the number of components 1,2, and 3 to
produce such that the total profit is maximized. No mathematical model is required. Only the
Excel model and solution is required. (2 points)
Optimal Production Quantities: Component 1: 1000, Component 2: 175, and Component 3: 200.
Total profit = $10850.
b.
If one more hour could be made available on the shaper, how much would it be worth? (1 point)
$45
Part II – Supplying Power at Midwest Electric (5 points)
Midwest Electric has three electric power plants that supply the power needs of four cities. Each power
plant can supply the amounts shown in the table below (in millions of kilowatt-hours of electricity):
Supply
Plant 1
40
Plant 2
50
Plant 3
40
The peak power demand (again in millions of kwh) at each city is given in the following table:
Demand
City 1
40
City 2
20
City 3
30
City 4
30
2
Finally, the cost (in dollars) of sending a million kwh from each plant to each city is given in the following
table:
City 1
City 2
City 3
City 4
Plant 1
8
6
10
9
Plant 2
9
12
13
7
Plant 3
12
9
16
5
a.
Midwest Electric wants to find the lowest-cost method for meeting the demand of the four cities. Towards that goal, determine the amount of electricity (in millions of kwh) that Midwest Electric should send from each of the plants to each of the cities. No mathematical model is required. Only the Excel model and solution is required.
(2 points)
Minimum total cost $1020.
b.
Identify the binding and the nonbinding constraints in your solution. (1 point)
All constraints are binding.
c.
If you had to decide to increase supply at only one of these plants, which one would you choose? Why? (1 points)
I would increase supply at plant 1 because it has the lowest shadow price.
d.
What happens to your solution if Plant 1 can only supply 20 M Kilowatt-hours of electricity? (1 point)
No feasible solution.
Part III – Hiker’s Bag (4 points)
A hiker has various cans of food of assorted sizes that are to be placed in a knapsack. Unfortunately, the knapsack is not large enough to hold all the cans. Therefore, the hiker must determine which cans are to
be included in the knapsack. Suppose that a hiker's knapsack will hold no more than 0 .8 cubic feet of canned goods. The hiker would like to make a selection that will maximize the total protein content of the food in the knapsack. The food items that are being considered for inclusion in the knapsack are shown in Table 7 .1.
3
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a.
How should the hiker pack his bag? In other words, which of item 1, 2, 3, 4, and 5 should
the hiker pack in this bag such that the total protein content is maximized. Keep in mind that only one of each item is available. (2 points)
Ans: Take 1 item 2 and 1 item 4. Total protein = 60 grams. b.
What happens to the solution if the hiker does not want to include
item 2 and 3 for sure? (1 point)
Ans: Pick item 1, 4 and 5. The total protein = 42 grams. c.
What happens to the solution if the hike decides to include at least one of can 1 or 2? (1
point)
Ans: Take 1 item 2 and 1 item 4. Total protein = 60 grams. 4