0
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Are you just looking for any possible scenario to fit this LP? $\endgroup$ – David Mar 29 '17 at 4:17
  • $\begingroup$ 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. $\endgroup$ – Anurabh Chakravarty Mar 29 '17 at 4:25
  • $\begingroup$ 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. $\endgroup$ – David Mar 29 '17 at 4:26
3
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Thanks a lot for your help. $\endgroup$ – Anurabh Chakravarty Mar 29 '17 at 4:43
  • $\begingroup$ @AnurabhChakravarty not a problem! When in doubt, for math programming problems, I immediately go to farmers, scheduling/staffing, or chemical mixing. They tend to yield very 'textbook' and overly simple problems, but for the sake of tests/quizzes they often suffice. $\endgroup$ – David Mar 29 '17 at 4:45
  • $\begingroup$ Do you teach mathematics? $\endgroup$ – Anurabh Chakravarty Mar 29 '17 at 4:48
  • $\begingroup$ @AnurabhChakravarty I'm in my last year of an operations research PhD program so I get stuck teaching courses from time to time. $\endgroup$ – David Mar 29 '17 at 4:49
  • 1
    $\begingroup$ Thanks again for your offer. I always have questions. You'll soon tire of them. I'll only be asking the one's which really perplex me. $\endgroup$ – Anurabh Chakravarty Mar 29 '17 at 4:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.