A farmer has 10 acres to plant in wheat and barley. He has to plant at least 7 acres. However, he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of barley costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of barley. If the profit is $500 per acre of wheat and $300 per acre of barley how many acres of each should be planted to maximize profit?

Construct the Linear programming model.