Originally Posted by

**ChristinaC20** I'm new to this site so I'm hoping this is the right area to post this. I'm dealing with a

**finite mathematics problem.** Okay so my professor made up a bunch of problems only thing is they are very different from the ones in our book so I'm not as sure how to go about them. The problem reads:

- A small country grows only 2 crops for export:coffee and cocoa. The country has 500,000 hectares of land available for the crops. Long term contracts require that at least 100,000 hectares of land be devoted to coffee and at least 200,000 hectares to cocoa. Cocoa must be processed locally and production conditions limit cocoa to 270,000 hectares. Coffee requires 2 workers per hectare and cocoa requires 5 workers per hectare. No more than 1,750,000 people are available for working these crops. Coffee produces a profit of $220 per hectare and cocoa a profit of $550 per hectare. How many hectares should the country devote to each crop in order to maximize profit?

I need to be able to:

- clearly define the two variables

- It's hard to give a "hint" for this- just do what it says. Since the question asked was "How many hectares should the country devote to each crop in order to maximize profit?", the two variables are x= "number of hectares devoted to coffee", y= "number of hectares devoted to cocoa".

- determine the system of constraints that models the situation.

Write things like "The country has 500,000 hectares of land available for the crops. Long term contracts require that at least 100,000 hectares of land be devoted to coffee and at least 200,000 hectares to cocoa. Cocoa must be processed locally and production conditions limit cocoa to 270,000 hectares." as inequalities. For example, "The country has 500,000 hectares of land available for the crops" means that, if x is the amount used for coffee and y the amount used for cocoa, then x+ y is the total hectares of land used for both: $\displaystyle x+ y\le 500,000$. The boundary of that is the straight line x+ y= 500,000. Since x= 0 y= 0 certainly satisfies x+ y< 500,000, the region satisfying x+ y< 500,000 is the side of that line containing (0,0).