# How do I convert the following Linear Programming Problem into a word problem?

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 : $$x_1,x_2,x_3\ge0$$

• Are you just looking for any possible scenario to fit this LP? – David Mar 29 '17 at 4:17
• It would be preferable if it were related to economics and the constraints were resource constraints. But any other scenario would be great too. I'm really in a fix. – Anurabh Chakravarty Mar 29 '17 at 4:25
• I've given a classic, "farmer-type" scenario, let me know if it is acceptable. This type of interpretation could be ported to any number of industries. – David Mar 29 '17 at 4:26

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?