A distributor of industrial chemicals with demand in six major cities is in the
ID: 444407 • Letter: A
Question
A distributor of industrial chemicals with demand in six major cities is in the process of setting up several manufacturing plants. It has five potential locations to choose from. The final choice of plant locations will be based on three factors: the monthly operating cost and capacities, which vary from location to location, and also the shipping costs to the demand cities. This information is summarized in the tables below.
Monthly
Monthly
Fixed
Capacity
Cost
in Tons
Location 1
$7,500
18
Location 2
$3,500
24
Location 3
$5,000
27
Location 4
$4,000
22
Location 5
$3,000
31
Shipping costs per ton between the proposed plant locations and demand cities
Location 1
Location 2
Location 3
Location 4
Location 5
MonthlyDemand
City 1
1600
1500
2000
400
900
10
City 2
400
1900
2400
1400
1600
8
City 3
700
1000
1400
500
700
12
City 4
1600
100
500
1000
500
6
City 5
1200
500
900
700
300
8
City 6
2800
1200
800
2300
1800
11
Find the locations where the plants should be opened so as to minimize monthly operating costs while meeting customer demand.
Monthly
Monthly
Fixed
Capacity
Cost
in Tons
Location 1
$7,500
18
Location 2
$3,500
24
Location 3
$5,000
27
Location 4
$4,000
22
Location 5
$3,000
31
Explanation / Answer
Location 5th has lower operating cost and It is meetin.g customer demand. After demand, Its capacity is higher. We got operating cost for five locations like total of location1(Sum of vertical line or shipping cost + fixed cost vertically) or sum of shipping cost and fixed cost for example .7500(Fixed cost+ 8300( shipping costor total of 1 city to 6 city=15800 and its capacity after deducting demandis 8, 3500+6200=9700, capacity after deducting demand is 16 capacity, 8000+5000=13000 , its capacity is 15, 6300+4000=10300 and its capacity is 14, 5800+3000=8800 and capacity after deducting demand drom capacity, its new capacity is 20. So location 5th has minimum operating cost and its capacity after deducting demand is 20 .
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