Problem 9-90

A last-minute proposal suggests balancing the number of food and medicine supplies. For instance, if a country gives 150 food packages, then they would also give 150 medicine packages. How many food and medicine packages should the United Nations require from each country in this case? Explain how you determined your solution. 

How we determined our constraints: 

• After completing the previous problems (9-88 & 9-89), we were able to create the given constraints of the regions needed in order to solve this problem. In problem 9-88 we were able to determine the lines of each country which represented how many food and medicine packages they can provide. By plotting these given lines we were then able to create a hexagon like region. 
• This region is then able to give us the  implied restrictions needed to solve the following problems, by analyzing the constraints, we are then able to easily find and use the process of elimination to find our answer. 
• In this case, our answer is a value found in the shaded hexagon region, that of which have the same values (when the plotting the X and Y, the values will be equivalent). Knowing this, we are then able to diminish and restrict our possible answers and find a conclusion more effectively. 

How we determined solutions:

• Answer 1: At first when solving this given problem we found a point at which we would use as a test evaluation. By doing this, we simply found a plot at which was located inside the shaded region. By doing this we would be able to deduce as to whether it was a viable answer or not and we would be able to determine more or so what the actual answer should be. We firstly plotted the point (200, 100), at which was located inside the region, although we later discarded answers similar to this coordinate due to the fact that it did not meet the requirements of the problem, being that the X and Y values needed to be equivalent. 
• Answer 2: Once determining that answers such as Answer 1 would not be a viable solution to this problem, we then assured to plot a point that of which had the same X and Y values. This being said we plotted the point (120, 120). This coordinate is located within the shaded region and follows all the problem constraints. Although, it is not the highest X and Y values when X and Y are equivalent, therefore a higher value solution is needed in order to solve this problem. 
• Answer 3: After testing two viable answers and deducing them as incorrect, we then found it easier as to analyze how far in the shaded region we could travel on the X-axis. This value ended up being 250, in which we did the same with the Y-axis, the value being 275. Although the point (250, 275) is not found on the shaded region, therefore we continued analyzing similar points, such as (200, 200). Once testing this given point we found that it was the same coordinate as that of a point on the red number line. Therefore indicating that this was the highest X and Y values that we could travel in the shaded region in order for these two variables to be the same amount.  

Final Answer:

After testing and selecting different possible solutions for this problem, we have been able to determine a viable answer after analyzing the given constraints of this problem. The constraints given were that of the X and Y values being equivalent, and the answer being found in the shaded region of the 6 lines previously plotted in problems 9-88 and 9-89. With this being said we found that each nation should be able to contribute 200 food packages and 200 medicine packages as a part of the last minute proposal. 

Completed by Kylie Rodriguez