The Salim Group is a major multinational conglomerate involved in five core sectors: plantations, property, industrial, motors and energy & utilities. The Salim Group wants to examine the economic feasibility of 1,600 hectares of available land in Johor, Malaysia, to plant two types of palm oil trees. The palm oil contains palmitate and oleate, which are used in the oleochemical industry. Palmitate and oleate contents of palm oil type 1 and type 2 from every hectare are presented in the table below:

Type 1 Type 2

Palmitate 45% 42%

Oleate 40% 43%

The company needs to obtain at least 1200 tons of palmitate and 950 tons of oleate.

Every hectare planted with palm trees type 1 is expected to yield 1.8 tons of crude palm oil from which palmitate and oleate are extracted. Similarly, every hectare planted with palm trees type 2 is expected to produce 1.7 tons of crude palm oil from which palmitate and oleate are derived. Preliminary estimations have shown that every hectare planted with palm tree type 1 requires 27.5 cubic meters of water per day and 1.35 tons of fertilizer. Every hectare planted with palm tree type 2 requires 15.6 cubic meters of water per day and with 1.15 tons of fertilizer. Researchers estimate that it will take 13 hours of labour to harvest each hectare planted with both palm trees type 1 and type 2. There are extraction costs. Every metric ton of yield from palm trees types 1 and 2 has extraction costs of $180 and $150, respectively.

Since the land has abundant water resources due to annual rainfall, The Salim Group planters can use as much water as they want. Also, the farmers can buy as much fertilizer as they need at the cost of 15 dollars per 25-kg bag. Finally, The Salim Group planters can hire labourers to harvest the fields at a rate of 8.5 dollars per hour. If the farmers sell all the palmitate and oleate that they extract, how many hectares of each type should The Salim Group plan to plant in the least costly manner?

Provide a brief specification for your model. It should include an introduction, assumptions, limitations, decision variables, objective function, and constraints