# Production Problem sheet

## Production Problem sheet

﻿MGMT2026 Problem Sheet Solution
Question 1
A) Precedence diagram

B) Required cycle time
8hrs *2 shift = 16hrs
16hr * 60mins = 960 mins
960mins/600 units = 1.6 mins
1.6 mins * 60 = 96 sec

C) Minimum work stations
20+30+25+10+55+3-+25+40 = 235
235/96 sec = 2.45 or 3 workstations

D) Balancing of lines

Workstation 1
Workstation 2
Workstation 3
96 seconds
96 seconds
96 seconds
B 30 sec 66sec
E 55 sec 41 sec
G 25 sec 71 sec
C 25 sec 41 sec
F 30 sec 11 sec
H 40 sec 31 sec
A 20 sec 21 sec
11 sec
31 sec
D 10 sec 11 sec

11 sec

= 53 idle time in all

E) Efficiency of the line
235/ (3 workstation * 96 sec) = 235/288 = 0.8159722222 or 1 (nearest whole number)
235/288*100 = 81.59% express as a percentage
Question 2
A) I) Total number of students
2500+1000+10000+4500+7500 = 25,500

II) Finding central office using center-of-gravity method
Location
X Coordinate
Y Coordinate
Size
X output
Y output
A
5
5
2500
5 * 2500
12500
5 * 2500
12500
B
0
5
1000
0 * 1000
0
5 * 1000
5000
C
0
0
10000
0 * 10000
0
0 *10000
0
D
5
0
4500
5 * 4500
22500
0 * 4500
0
E
2
1
7500
2 * 7500
15000
1 * 7500
7500
Total
12
11
25500
50000
25000

50000/25500 = 1.96

25000/ 25500 = 0.98

New location (1.96, 0.98) or (2,1) which would be location E.

B) I) Equation for total cost
Facility 1: 500,000 + 25U = TC
Facility 2: 800,000 + 22U = TC

II)
Facility
FC per year
VC per unit
1
500,000
25
2
800.000
22

F1 vs. F2
500,000 + 25U = 800,000 + 22U
25U – 22U = 800,000 – 500,000
3U = 300,000
Units = 100,000

Facility
Output
FC
VC
TVC
TC
1
0
500,000
25
0
500,000

100,00

25
2,500,000
3,000,000
2
0
800,000
22
0
800,000

100,000

22
2,200,000
3,000,000

III) Facility 1 would be superior when output...