# Mission College Application of Linear Algebra Questions

User Generated

dhr_athlra

Mathematics

Mission College

## Description

. Casper Geriatric Center, a senior medical facility located in a large hospital in New Zealand, started a procedure where their guests receive their meals in their rooms while the food is still as hot as possible. The facility will continue to prepare the food in the commissary, but will now deliver it in bulk (not individual servings) to one of three new meal serving stations in the building. From there, the food will be reheated, meals will be placed on individual trays, loaded onto a cart, and distributed to the various floors and sections of the facility.

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The three new serving stations are as efficiently located as possible to reach the various hallways in the facility. The purpose of the new procedure is to increase the temperature of the hot meals that the guest receives. Therefore, the amount of time needed to deliver a tray from a serving station will determine the proper distribution of food from serving station to section. The table below summarizes the time associated with each possible distribution channel.

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DISTRIBUTION TIME (minutes)

TO:   DESTINATIONS

FROM:

SOURCES

Section   A

Section   B

Section   C

Section   D

Section   E

Section   F

Station   10J

12

11

8

9

6

6

Station   6G

6

12

7

7

5

8

Station   2L

8

9

6

6

7

9

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Station 10J can supply 200 meals. Station 6G can produce 225. The maximum that Station 2L can prepare is 275. This month, there are 700 guests in the facility, 30% are in Section D, 160 are divided equally in Sections A and F, Section B has 120, Section C has 30 more patients than Section B, and the rest are in Section E.

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1) Is this a balanced or unbalanced problem?

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2) Is it a minimization or maximization problem?

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Hey there , please find attached solution

Question 2

1. This is a balanced problem

2. This is a minimization problem
3. This is a balanced problem because the total capacity (200 + 225 + 275) is equal to
the
demand (700 guests). It is a minimization problem because the objective of the new
setup is
to deliver food to guests at the highest temperature possible and so the distribution
time
has to be minimal.

Question 3

The capacity of stations 10J and 6G is 425 meals ie 200 + 225

Question 4

The optimal solution is 4 825 / 60 hours = 80 hours (rounded to nearest hour

Please refer to attached spreadsheet, the objective is to minimize the distribution time.

Question 5

D will get meals from Stations 6G and 2L, 145 and 65 meals from each station respectively

Question 6

This is a minimal spanning problem : True

Question 7

There are 16 branches in the network listed as below

12 13 15 24 34 35 45 410

57 56 67 610 78

79 89 910

Question 8

Time taken to drive through 2-4-8 is the summation of time taken from 2 to 4 and from 4 to 8

5 minutes + 10 minutes

Time taken

=

=

15 minutes

0.25 hours

Question 9

Arc 6-10 takes the longest to travel (40 minutes)

Question 10

The optimal solution is 60 minutes following the path below :

1 - 2 - 4 - 8 - 9 - 10 . This is deduced by Dijkstra Algorithm which will determine
The shortest distance between given points , starting from a source point

Question 11

ASSIGNMENT PROBLEMS
Programs
Group 1 32

35

15

27

Group 2 38

40

18

35

Group 3 41

42

25

38

Group 4 45...

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