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A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of \$50 and each acre of barley yields a profit of \$70. To sow the crop, two machines, a tractor and tiller, are rented. The tractor is available for 200 hours, and the tiller is available for 100 hours, Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. How many acres of each crop should be planted to maximize the farmer's profit?

I'll try to use simplex method, afterwards.

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The first step is to describe what your variables are: $x$ which could be the number of acres of Barley sown, and $y$ which could be the number of acres of wheat.

Now, what is the profit function: $P = 70x + 50y$ (70 dollars per acre of barley + 50 dollars per acre of wheat).

Now, what are the constraints: certainly $x\geq 0$ and $y\geq 0$. What about not overusing the tiller?

$$2x + 1y \leq 100$$ 2 hours on tiller for each acre of barley, 1 hour for each acre of wheat... not more than 100 hours available.

Similarly, what about not overusing the tractor?

$$3x + 4y \leq 200$$ 3 hours on tractor for each acre of barley, 4 hours on the tractor for each acre of wheat... not more than 200 hours total on the tractor.

Condensing all those constraints you have:

Maximize $P=70x + 50y$

Subject to \begin{align*} 2x + 1y &\leq 100 \\ 3x + 4y &\leq 200 \\ x, y &\geq 0 \end{align*}

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