Question 17 ) The president of a consulting firm wants to minimize the total num
ID: 375395 • Letter: Q
Question
Question 17) The president of a consulting firm wants to minimize the total number of hours it will take to complete four projects for a new client. Accordingly, she has estimated the time it should take for each of her top consultants—Charlie, Gerald, Johnny, and Rick—to complete any of the four projects, as follows:
Project Hours
Consultant
A
B
C
D
Charlie
13
16
11
18
Gerald
13
15
10
12
Johnny
15
11
20
15
Rick
17
17
12
22
What is the optimal assignment of consultants to projects? (Use the assignment method.)
Question 21) A manufacturing company preparing to build a new plant is considering three potential locations for it. The fixed and variable costs for the three alternative locations are presented below.
a. Complete a numeric locational cost-volume analysis.
b. Indicate over what range each of the alternatives A, B, C is the low-cost choice.
c. Is any alternative never preferred? Explain.
Costs
A
B
C
Fixed ($)
2,500,000
2,000,000
3,500,000
Variable ($ per unit)
21
25
15
Project Hours
Consultant
A
B
C
D
Charlie
13
16
11
18
Gerald
13
15
10
12
Johnny
15
11
20
15
Rick
17
17
12
22
Explanation / Answer
17.
The problem is of minimization
Intially to solve the problem by assignment method.
Let us consider as:
Further, let is rename the jobs of consultants as:
A: I
B: II
C : III
D : IV
SOLUTION:
Solution:
The number of rows = 4 and columns = 4
I
II
III
IV
A
13
16
11
18
B
13
15
10
12
C
15
11
20
15
D
17
17
12
22
Here given problem is balanced.
Step-1: Find out the each row minimum element and subtract it from that row
I
II
III
IV
A
2 2=13-11
5 5=16-11
0 0=11-11
7 7=18-11
(-11)
B
3 3=13-10
5 5=15-10
0 0=10-10
2 2=12-10
(-10)
C
4 4=15-11
0 0=11-11
9 9=20-11
4 4=15-11
(-11)
D
5 5=17-12
5 5=17-12
0 0=12-12
10 10=22-12
(-12)
Step-2: Find out the each column minimum element and subtract it from that column.
I
II
III
IV
A
0 0=2-2
5 5=5-0
0 0=0-0
5 5=7-2
B
1 1=3-2
5 5=5-0
0 0=0-0
0 0=2-2
C
2 2=4-2
0 0=0-0
9 9=9-0
2 2=4-2
D
3 3=5-2
5 5=5-0
0 0=0-0
8 8=10-2
(-2)
(-0)
(-0)
(-2)
Step-3: Make assignment in the opporunity cost table
(1) Rowwise cell (C,II) is assigned
(2) Rowwise cell (D,III) is assigned, so columnwise cell (A,III),(B,III) crossed off.
(3) Columnwise cell (A,I) is assigned
(4) Columnwise cell (B,IV) is assigned
Rowwise & columnwise assignment shown in table
I
II
III
IV
A
[0] (3) Column wise cell (A,I) is assigned
5
0 Column wise (A,III) crossed off because
(2) Row wise cell (D,III) is assigned
5
B
1
5
0 Column wise (B,III) crossed off because
(2) Row wise cell (D,III) is assigned
[0] (4) Column wise cell (B,IV) is assigned
C
2
[0] (1) Row wise cell (C,II) is assigned
9
2
D
3
5
[0] (2) Row wise cell (D,III) is assigned
so columnwise cell (A,III),(B,III) crossed off.
8
Step-4: Number of assignments = 4, number of rows = 4
Which is equal, so solution is optimal
Optimal assignments are
I
II
III
IV
A
[0] Original cost 13
5 Original cost 16
0 Original cost 11
5 Original cost 18
B
1 Original cost 13
5 Original cost 15
0 Original cost 10
[0] Original cost 12
C
2 Original cost 15
[0] Original cost 11
9 Original cost 20
2 Original cost 15
D
3 Original cost 17
5 Original cost 17
[0] Original cost 12
8 Original cost 22
Optimal solution is
Work
Job
Cost
A
I
13
B
IV
12
C
II
11
D
III
12
Total
48
Let us now rename again in the final table:
Work
Job
Cost
Charlie
A
13
Gerald
D
12
Johnny
B
11
Rick
C
12
Total
48
Hence, the assignments to consultants to be allocated as above table to minimize the total number of hours as:
Charlie: A
Gerald: D
Johnny: B
Rick: C
21.
Hence, B is cheapest up to 125,000 units; C is cheapest after 166,667 units. A is cheapest in between. The B-C crossover is not relevant.
I
II
III
IV
A
13
16
11
18
B
13
15
10
12
C
15
11
20
15
D
17
17
12
22
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