A food is manufactured by refining raw oils and blending them together. The raw oils come in two categories; Vegetable oils (VEG1 and VEG2), and Non-vegetable oils (OIL1, OIL2, and OIL3). 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 and no more than 250 tons of non-vegetable oils. There is no loss of weights in the refining process and the cost of refining may be ignored. There is a technical restriction of hardness in 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. The costs (per ton) and hardness of the raw oils are: VEG1 VEG2 OIL1 OIL2 OIL3 Cost ($) 110 120 130 110 115 Hardness 8.8 6.1 2.0 4.2 5.0 The final product sells for $150 per ton. Formulate this problem as a linear programming model to determine how much to make of each product so as to maximize their net profit.