5. Heart Beats is a manufacturer of medical equipment. The company's primary product is a device used to monitor the heart during medical procedures. This device is produced in two factories and shipped to two warehouses. The product is then shipped on demand to four third-party wholesalers. All shipping is done by truck. The product distribution network is shown below. The annual production capacity at Factories 1 and 2 is 400 and 250, respectively. The annual demand at Wholesalers 1, 2, 3, and 4 is 200, 100, 150, and 200, respectively. The cost of shipping one unit in each shipping lane is shown on the arcs. Due to limited truck capacity, at most 250 units can be shipped from Factory 1 to Warehouse 1 each year. [400] F1 [400] F1 [250] F2 [250] F2 $40 [250] [0] WH 1 WH 2 $25 [0] $35 [0] WH 1 WH 2 [0] WS 1 WS 2 WS 3 $60 WS 4 $55 [-200] [-100] (a) Ignore the arrow of each arc (or in other words, treat this as a undirected network), find the minimum spanning tree, what is the cost? (b) Given the basic arcs are: F1 → WH2, F2 → WH2, WH1 → WS1, WH1 → WS2, WH2 → WS2, WH2 → WS3, WH2 → WS4. Find a BF solution. [-150] $35 [-200] $50 $65 WS 1 $5 WS 2 WS 3 WS 4 [-200] [-100] [-150] [-200]

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5. Heart Beats is a manufacturer of medical equipment. The company's primary product is a
device used to monitor the heart during medical procedures. This device is produced in
two factories and shipped to two warehouses. The product is then shipped on demand to
four third-party wholesalers. All shipping is done by truck. The product distribution
network is shown below. The annual production capacity at Factories 1 and 2 is 400 and
250, respectively. The annual demand at Wholesalers 1, 2, 3, and 4 is 200, 100, 150, and
200, respectively. The cost of shipping one unit in each shipping lane is shown on the
arcs. Due to limited truck capacity, at most 250 units can be shipped from Factory 1 to
Warehouse 1 each year.
[400] F1
[400] F1
[250] F2
[250] F2
$40
[250]
[0]
WH
1
$25
WH
2
[0]
$35
[0]
WH
1
WH
2
[0]
WS
1
WS
2
WS
3
$60
WS
4
$55
[-200]
[-100]
[-150]
$35
(a) Ignore the arrow of each arc (or in other words, treat this as a undirected network), find the
minimum spanning tree, what is the cost?
(b) Given the basic arcs are: F1 → WH2, F2 WH2, WH1 → WS1, WH1 → WS2, WH2 →
WS2, WH2 → WS3, WH2 → WS4. Find a BF solution.
[-200]
$50
$65
WS
1
$5
WS
2
WS
3
WS
4
[-200]
[-100]
[-150]
[-200]
Transcribed Image Text:5. Heart Beats is a manufacturer of medical equipment. The company's primary product is a device used to monitor the heart during medical procedures. This device is produced in two factories and shipped to two warehouses. The product is then shipped on demand to four third-party wholesalers. All shipping is done by truck. The product distribution network is shown below. The annual production capacity at Factories 1 and 2 is 400 and 250, respectively. The annual demand at Wholesalers 1, 2, 3, and 4 is 200, 100, 150, and 200, respectively. The cost of shipping one unit in each shipping lane is shown on the arcs. Due to limited truck capacity, at most 250 units can be shipped from Factory 1 to Warehouse 1 each year. [400] F1 [400] F1 [250] F2 [250] F2 $40 [250] [0] WH 1 $25 WH 2 [0] $35 [0] WH 1 WH 2 [0] WS 1 WS 2 WS 3 $60 WS 4 $55 [-200] [-100] [-150] $35 (a) Ignore the arrow of each arc (or in other words, treat this as a undirected network), find the minimum spanning tree, what is the cost? (b) Given the basic arcs are: F1 → WH2, F2 WH2, WH1 → WS1, WH1 → WS2, WH2 → WS2, WH2 → WS3, WH2 → WS4. Find a BF solution. [-200] $50 $65 WS 1 $5 WS 2 WS 3 WS 4 [-200] [-100] [-150] [-200]
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