A food is manufactured by refining raw oils and blending them together.[2] The raw oils come in two categories:
|
vegetable oils |
VEG 1 |
|
VEG 2 |
|
|
non-vegetable oils |
OIL 1 |
|
OIL 2 |
|
|
OIL 3 |
Each oil may be purchased for immediate delivery (January) or bought on the futures market for delivery in a subsequent month. Prices now and in the futures market are given below (in £/ton):
|
VEG 1 |
VEG 2 |
OIL 1 |
OIL 2 |
OIL 3 |
|
|
January |
110 |
120 |
130 |
110 |
115 |
|
February |
130 |
130 |
110 |
90 |
115 |
|
March |
110 |
140 |
130 |
100 |
95 |
|
April |
120 |
110 |
120 |
120 |
125 |
|
May |
100 |
120 |
150 |
110 |
105 |
|
June |
90 |
100 |
140 |
80 |
135 |
The final product sells at £150 per ton.
Vegetable oils and non-vegetable oils require different production lines for refining. In any month it is not possible to refine more than 200 tons of vegetable oils and more than 250 tons of non-vegetable oils. There is no loss of weight in the refining process and the cost of refining may be ignored.
It is possible to store up to 1000 tons of each raw oil for use later. The cost of storage for vegetable and non-vegetable oil is £5 per ton per month. The final product cannot be stored, nor can refined oils be stored.
There is a technological restriction of hardness on the final product. In the units in which hardness is measured this must lie between 3 and 6. It is assumed that hardness blends linearly and that the hardnesses of the raw oils are
|
VEG 1 |
8.8 |
|
VEG 2 |
6.1 |
|
OIL 1 |
2.0 |
|
OIL 2 |
4.2 |
|
OIL 3 |
5.0 |
What buying and manufacturing policy should the company pursue in order to maximize profit?
At present there are 500 tons of each type of raw oil in storage. It is required that these stocks will also exist at the end of June.