COMPUTER PRODUCTION MVE Enterprises can manufacture four different computer mode
ID: 443172 • Letter: C
Question
COMPUTER PRODUCTION
MVE Enterprises can manufacture four different computer models; the Student, Plus, Net, and Pro models. The following gives the configurations of each model:
STUDENT
PLUS
NET
PRO
Processor
Celeron
Celeron
Celeron
Pentium
Hard Drive
20 gb
20 gb
20 gb
30 gb
Floppy Drives
1
1
2
1
Zip Drives
Yes
Yes
No
Yes
Audio/Video
CD R/W
DVD
DVD +
CD R/W
DVD +
CD R/W
Monitor
15”
15”
17”
17”
Case
Tower
Mini-
Tower
Mini-
Tower
Tower
Production
Time (hrs.)
.4
.5
.6
.8
Unit Profit
$70
$80
$130
$150
MVC must satisfy a contract that produces a minimum of 100 Net models per week
MVC employs 25 workers, each of whom averages 30 production hours each per week
The following resources are available weekly:
Processors
Hard Drives
Other Drives
Celeron - 700
20 gb – 800
Floppy – 1600
Pentium - 550
30 gb – 950
Zip – 1000
Audiovisual
Monitors
Cases
CD / R/W – 1600
15” – 850
Mini – Tower – 1250
DVD – 900
17” – 800
Tower - 750
a. Determine the optimal weekly production schedule for MVC. What is the optimal weekly profit?
b. What is the minimum price that would justify producing the Plus model? Explain.
c. If MVC could purchase additional 17” monitors for $15 more than what they are currently paying for them, should they do this? Explain.
d. Suppose an additional worker could be hired for $1000 per week over the existing weekly worker salary. (Recall that workers average 30 hours per week.) Should MVC do this? Explain.
STUDENT
PLUS
NET
PRO
Processor
Celeron
Celeron
Celeron
Pentium
Hard Drive
20 gb
20 gb
20 gb
30 gb
Floppy Drives
1
1
2
1
Zip Drives
Yes
Yes
No
Yes
Audio/Video
CD R/W
DVD
DVD +
CD R/W
DVD +
CD R/W
Monitor
15”
15”
17”
17”
Case
Tower
Mini-
Tower
Mini-
Tower
Tower
Production
Time (hrs.)
.4
.5
.6
.8
Unit Profit
$70
$80
$130
$150
Explanation / Answer
This is a product mix problem, we are supposed to find the optimal weekly production schedule for MVC.
Decision variables are the quantities of each type of computers to be produced weekly. let a, b, c and d represents the number of Student, Plus, Net and Pro models respectively to be produced weekly.
Objective function - As unit profit figures are given for each type of model of computers, therefore Profit Maximization is the objective, say Maximize Z = 70a +80b + 130c + 150d
Constraints- There are number of constraints on account of manpower, processors and other components and minimum production of 100 Net model as stated below:
c >= 100 ( minimum 100 net model)
.4a + .5b + .6c + .8d <= 750 (avalability of workers hours)
a + b + c <= 700 and d <= 550 ( processor availability )
a + b + c < = 800 and d <= 950 (hard drive availability)
a + b+ 2c + d <= 1600 ( floppy availability)
a+b+d <= 1000 (zip drive)
a+c <=1600 and b+c+d <=900 C R/W and DVD
a+b <=850 and c+d <=800 Number of monitors
a+d <= 750 and b+c <=1200 Types of case Tower and Mini-tower
lastly a, b, c and d >= 0 Non negativity constraint being quantities.
Solution: Optimal solution
Variable Value Reduced Cost Original Val Lower Bound Upper Bound
a 275 0 70 20 180
b 100 0 80 25 130
c 325 0 130 80 220
d 475 0 150 60 200
Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound
labor hours 0 15 750 735 Infinity
c1 25 0 700 150 800
c2 0 100 1,600 1,500 Infinity
c3 0 150 1,000 850 Infinity
c4 0 525 1,600 1,075 Infinity
c5 55 0 900 800 937.4999
c6 0 475 850 375 Infinity
c7 50 0 800 650 900
c8 45 0 750 200 800
c9 0 825 1,250 425 Infinity
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