1.Transporting Units . Your company builds computers at three locations (Plant 1
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Question
1.Transporting Units. Your company builds computers at three locations (Plant 1-Plant 3) and ships it to five distributors (D1-D5). The cost per unit of building a computer and the production capacity for each plant are known. The number of units demanded by each customer is also known. The cost (in dollars) of shipping unit from a plant to each distributor is available as well. The following table provides the data:
D1
D2
D3
D4
D5
Capacity
Cost
From P1
$23
$21
$21
$16
$15
78
$236
From P2
$19
$19
$25
$17
$23
86
$238
From P3
$18
$19
$15
$16
$16
80
$279
Demands
39
47
50
47
36
Your company wishes to minimize the cost of producing and shipping computers from its plants to its distributors. What is the minimum total cost? What will be the cost of production? What is the cost of shipping?
2.Assigning Engineers. Your company has 4 senior engineers (E1 – E 4) available to work on the firm’s 4 current projects (P1-P4) over the next 2 weeks. The firm’s chief engineer has developed the following table of quality scores, which show each engineer’s quality on each type of project, on a scale of 100. Also shown is the estimate of the time (in hours) required for each project.
P1
P2
P3
P4
Engineer 1
69
57
59
66
Engineer 2
50
35
72
73
Engineer 3
33
83
81
80
Engineer 4
39
32
75
73
Time
95
66
78
71
a. Assume that one engineer is assigned to each project. What assignment of engineers to projects maximizes the sum of the quality scores assigned?
b. Suppose that each engineer has 80 hours available over the next two weeks. Assuming that more than one engineer can work on a project, what assignment schedule maximizes the sum of quality scores assigned?
You only need to submit a write-up for part b. (You should submit an Excel solution for both part a) and b).
Note: To determine the amount of quality an engineer gives to a project, just multiply the quality for that project times the number of hours assigned. For example, if E1 works 30 hours on P1 and 50 hours on P2, he has added 30*77 quality to P1, and 50*29 quality to P2.
Hint: In Excel, create different tabs for part a. and b. Solve independently of each other.
D1
D2
D3
D4
D5
Capacity
Cost
From P1
$23
$21
$21
$16
$15
78
$236
From P2
$19
$19
$25
$17
$23
86
$238
From P3
$18
$19
$15
$16
$16
80
$279
Demands
39
47
50
47
36
Explanation / Answer
P1
P2
P3
P4
Engineer 1
69
57
59
66
Engineer 2
50
35
72
73
Engineer 3
33
83
81
80
Engineer 4
39
32
75
73
Time
95
66
78
71
P1
P2
P3
P4
Engineer 1
69
57
59
66
Engineer 2
50
35
72
73
Engineer 3
33
83
81
80
Engineer 4
39
32
75
73
Time
95
66
78
71
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