Maximize $$z=2x_1+10x_2+15x_3$$ Subject to : $$\begin{align} 3x_1+x_2+5x_3&\le55\\ 2x_1+x_2+x_3&\le26\\ x_1+x_2+3x_3&\le30\\ 5x_1+2x_2+4x_3&\le57 \end{align}$$ With non-negetivity constraints : $$x_1,x_2,x_3\ge0$$
2026-03-28 11:42:09.1774698129
How do I convert the following Linear Programming Problem into a word problem?
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A farmer has $55$ kg of fertilizer, $26$ kg of pesticide, $30$ kg mulch, and $57$ days worth of labor. The farmer intends on growing wheat, corn, and barley. For every square kilometer of wheat, the farmer must use $3$ kg of fertilizer, $2$ kg of pesticide, a kg of mulch, and $5$ days of labor. For corn, it requires $1$,$1$,$1$,$2$...etc., At the end of the season, every square kilometer of wheat can be sold for \$$2$ thousand, corn for \$$10$ thousand, and barley for \$$15$ thousand. How many square kilometers of each type of plant should the farmer grow to maximize his revenue?
An added benefit of this particular interpretation is it is reasonable to assume that the decision variables can be (approximately) continuous.