Reference no: EM131441278
A food is manufactured by rening raw oils and blending them together. The raw oils come in two categories:
Vegetable oil: VEG1, VEG2
Non-vegetable oil: OIL1, OIL2, OIL3
The prices for buying each oil are given below (in $/tonne)
VEG1 VEG2 OIL1 OIL2 OIL3
115 128 132 109 114
The final product sells at $180 per tonne. Vegetable oils and non-vegetable oils require different production lines for refining. It is not possible to rene more than 210 tonnes of vegetable oils and more than 260 tonnes of non-vegetable oils. There is no loss of weight in the refining process and the cost of refining may be ignored.
There is a technical restriction relating to the hardness of the final product. In the units in which hardness is measured this must lie between 3.5 and 6.2. It is assumed that hardness blends linearly and that the hardness of the raw oils is:
VEG1 VEG2 OIL1 OIL2 OIL3
8.8 6.2 1.9 4.3 5.1
It is required to determine what to buy and how to blend the raw oils so that the company maximizes its profit.
The following extra conditions are also imposed on this food manufacture problem stated above as a result of the production process involved:
the food may never be made up of more than 3 raw oils
if an oil (vegetable or non-vegetable) is used, at least 30 tonnes of that oil must be used Formulate the whole problem as an optimization model by deciding how much of each type of raw oil to be used (follow the 5 steps; you may need to introduce binary variables for those extra conditions).
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Food is manufactured by rening raw oils and blending
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