Well, I am not going to provide the solution for you without any thinking on your part.
You need to define the constraints and cost equations, and as they are stated pretty clearly, it should not be difficult.
Lastly, you need the Profit function, and mazimize it.
There are tools readily available for the solution after that. There are about 100 ways to do that, but one of the quickest is https://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue
If you need more help with your thinking, ask on that. here I think you are looking for optimum number of acres allocated to each of the of the crops, not exactly what you said in the last sentence.
a farmer has 20 hectares farm. he produces cabbage,carrot and potato. whatever he produces is fully sold in the market. he gets $ 4 per per kg for cabbage, 6 for carrot per kg and 5 for potato per kg. the average per hectare yield is 200kg of cabbage,250 kg of carrot and 150 kg of potato. to produce each of 20 kg of cabbage and carrot and 25 kg of potato, an amount of 10 birr respectively has to be used for fertilizer. labor required for each hectare to raise the vegetables is 5 man days for cabbage and potato each and 6 man days for carrot. a total of 300 man days of labor at a rate of 30 per man day are available. formulate this LPM that helps to determine the optimum number of hectares to maximize the farmer's total profit.
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I am only confused because it's profit maximization, with no profit
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