Roads for your construction company currently have three construction jobs in No
ID: 403321 • Letter: R
Question
Roads for your construction company currently have three construction jobs in Northeast Florida requiring crushed lime rock. Three pits are available to service the company%u2019s needs. The sources, destinations, tonnage available and cost per ton of shipment are given in the table below.
Sources
Destinations
Max tonnage available
From
cost per ton
to Job 1
to Job 2
to Job3
Pit Starke
$6
$9
$10
150
Pit Baldwin
$10
$11
$11
175
Pit Jonesville
$4
$5
$12
355
Job needs
200
100
300
600
A. Determine the optimal shipping assignment to minimize cost, based on shipping costs alone.
B. The cost per ton to purchase the rock differs from pit to pit.
Starke charges $0.67 per ton
Baldwin $0.65 per ton
and Jonesville charges $0.80 per ton.
C. Does this change the shipping assignment for minimizing costs? If so, what is the new assignment?
Sources
Destinations
Max tonnage available
From
cost per ton
to Job 1
to Job 2
to Job3
Pit Starke
$6
$9
$10
150
Pit Baldwin
$10
$11
$11
175
Pit Jonesville
$4
$5
$12
355
Job needs
200
100
300
600
Explanation / Answer
The firm should ship from Pit Jonesville to Job 1 and Job 2. For job 3, 150 ton from Pit Starke and 150 ton from Pit Baldwin. For job 1 and job 2, the shipment from Pit Jonesville is the chepest and Pit Jonesville has enough supply for both of the jobs. Shipment from Pit Starke to job 3 is the cheapest but it can only fulfill half of the demand. Therefore, the other half of material should ship from Pit Baldwin.
The cost will be,
Job 1 = 4 * 200 = 800
Job 2 = 5 * 100 = 500
Job 3 = 150 * 10 + 150 * 11 = 3,150
C) It has no affect on the previous shipping assignment, after the surcharges, shipment from Jonesville to job 1 and job 2 still the cheapest compare to the other 2 pit. Similar situation happens for job 3 too.
Now, new cost will be
Job 1 = 4.80 * 200 = 960
Job 2 = 5.80 * 100 = 580
Job 3 = 150 * 10.67 + 150 * 11.65 = 3,348
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