A mining company owns six iron mines, from each of which one ore can be extracted. Different

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Question:

A mining company owns six iron mines, from each of which one ore can be extracted. Different minerals have different properties. The percentage of iron per tonne of ore, the oxide content per tonne of ore, and the sulphur content per tonne of ore, for each of the ores, are given in the following table.

Minerals	Iron (%/tonne)	Oxide (%/tonne)	Sulphur(%/tonne)
1	67.7	19	2.5
2	65	17	1.2
3	62.9	16	2.4
4	63.0	11	2.5
5	62.6	14	2.2
6	63.4	15	0.7

Every day, the company has to mix these ores at the sorting centre in order to be able to sell them through 2 types of blends whose characteristics and selling prices must meet the following characteristics:

	Iron (% min /tonne)	Oxide (% max/tonne)	Sulphur (% max/tonne)
Mix 1	63	15.5	2.3
Mix 2	63.5	15	1.8

It is assumed that these blends can be sold on a daily basis.

It is assumed that these blends can be sold daily. It is not concerned here with the way in which these blends are delivered to the market. The ores are brought to the processing centre by means of three types of load, each of which is

3containing a precise quantity (in tonnes) of each of the ores.

These quantities and the costs for a unit of each type of load are given in the following table:

	Mineral 1	Mineral 2	Mineral 3	Mineral 4	Mineral 5	Mineral 6	Cost per load
Load 1	1	2	2	1	1	2	1050
Load 2	2	3	1	2	0.5	1	1200
Load 3	1	2	3	2	1	2	1300

For example, a Type 1 load is composed of 1 tonne of ore 1, 2 tonnes of ore 2, 2 tonnes of ore 3, 1 tonne of ore 4, 1 tonne of ore 5, 2 tonnes of ore 6. Each day, the

company may bring more than one load of each type to the sorting plant. The number of daily loads cannot exceed 30. In addition, a storage centre juxtaposed to the sorting plant allows the storage of ores from one day to the next. This centre has a limited capacity. It can store, free of charge, up to 15 tonnes of Ore 1, or 13 tonnes of Ore 2, or 12.5 tonnes of Ore 3, or 14 tonnes of Ore 4, or 12 tonnes of Ore 5, or 13.5 tonnes of Ore 6, or any equivalent combination. This means that several ores can be stored at the storage centre and one tonne of one ore does not occupy the same space as one tonne of another ore. For example, Ore 2 occupies 15/13 times more space than one tonne of Ore 1. Because loads arrive with fixed quantities of ore (Table 3), storage capacity may be exceeded. In this case, the excess ore is considered to be lost.

We ask that you write a linear model in compact form to plan the optimal production of the company's 2 blends for a given week. This is the one that maximizes the net revenue over 5 days, assuming that at the beginning of the week there are no ores in stock.