(10 pts) Consolidated Mining Company mines zinc ore at two locations: Blue Mesa (New Mexico) and Dry Pass (Washington State). Once mined, each ton of ore must be moved to one of two processing plants, one near Boise (Idaho), and the other in West Texas. The processed ore is then shipped to three customers, Galvanic Industries, MunchCo, and American Metals. These customers require 600, 400, and 700 tons per day of processed ore, respectively. Blue Mesa can produce up to 800 tons of ore per day at a cost of $12/ton. Dry pass can produce up to 1000 tons of ore per day at a cost of $10/ton. The Boise plant can process up to 1000 tons of ore per day at a cost of $17/ton. The West Texas plant can handle up to 700 tons per day at $15/ton. Shipping costs per ton between the mines, plants, and customers are given in the following two tables: From Blue Mesa From Dry Pass To GalvanicTo MunchCoTo American Metals Shipping cost to Boise$ 4.5$ 3.50 Shipping cost from Boise$ 2.25$ 3.35$ 6.00 Shipping cost to West TX$ 3.00$ 6.00 Shipping cost from West TX$ 5.75$ 2.95$ 7.10 What pattern of production, processing, and shipping will allow the firm to meet customer demands at the lowest possible cost? (a) Define decision variables.(b) Write a suitable LP problem formulation.
(10 pts) Consolidated Mining Company mines zinc ore at two locations: Blue Mesa (New Mexico) and Dry Pass (Washington State). Once mined, each ton of ore must be moved to one of two processing plants, one near Boise (Idaho), and the other in West Texas. The processed ore is then shipped to three customers, Galvanic Industries, MunchCo, and American Metals. These customers require 600, 400, and 700 tons per day of processed ore, respectively. Blue Mesa can produce up to 800 tons of ore per day at a cost of $12/ton. Dry pass can produce up to 1000 tons of ore per day at a cost of $10/ton. The Boise plant can process up to 1000 tons of ore per day at a cost of $17/ton. The West Texas plant can handle up to 700 tons per day at $15/ton. Shipping costs per ton between the mines, plants, and customers are given in the following two tables:
From Blue Mesa From Dry Pass
To Galvanic
To MunchCo
To American Metals
Shipping cost to Boise
$ 4.5
$ 3.50
Shipping cost from Boise
$ 2.25
$ 3.35
$ 6.00
Shipping cost to West TX
$ 3.00
$ 6.00
Shipping cost from West TX
$ 5.75
$ 2.95
$ 7.10
What pattern of production, processing, and shipping will allow the firm to meet customer demands at the lowest possible cost?
(a) Define decision variables.
(b) Write a suitable LP problem formulation.
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