- 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".
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: . 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).
- determine the system of constraints that models the situation.
Since the problem is to maximize profit, the "object function" is the profit. If x hectares are devoted to coffee and y hectares are devoted to cocoa, how much profit is made? Of course, you get that from "Coffee produces a profit of $220 per hectare and cocoa a profit of $550 per hectare."
- determine the objective function for the situation
Yes, each constraint will graph as one side of a straight line. You might do that by graphing the straight line, then shading the approriate side. If you use different "shading" (vertical lines, horizontal lines, diagonal lines, etc.) the "feasible region" will be the region with all the different shadings.
- Graph and shade the feasible solutions region (which i think i can handle if i had the right system of constraints)
Finding the corner points involves solving the two equations representing the lines that intersect at that corner.
- Evaluate the objective function for each of the corner points. (have serious problems with)
- Determine the values of the variables that will optimize the objective function.
Once you have done the previous part, see which corner point gives the largest value. The (x, y) values for that point are the values of the variables you want.
Can anyone help me figure this out without just giving me the answer , kinda like help me out step by step?Thanks.