SOLUTION: Nicholas does not want to spend more than $140 on bags of fertilizer and peat moss for his garden. Fertilizer costs $5 a bag and peat moss costs $14 a bag. Nicholas's van holds at

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Nicholas does not want to spend more than $140 on bags of fertilizer and peat moss for his garden. Fertilizer costs $5 a bag and peat moss costs $14 a bag. Nicholas's van holds at       Log On


   

Question 1205774: Nicholas does not want to spend more than $140 on bags of fertilizer and peat moss for his garden. Fertilizer costs $5 a bag and peat moss costs $14 a bag. Nicholas's van holds at most 20 bags.
Graph the system on your own graph paper with fertilizer as the independent variable and peat moss as the dependent variable. Then, decide which of the four graphs below shows the correct lines (dotted/solid), and then choose the letter for the region on that graph that should be shaded for the solution. If no regions should be shaded, choose No Solution.

Can he buy 13 bags of fertilizer and 7 bags of peat moss?
Can he buy 14 bags of fertilizer and 4 bags of peat moss?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Obviously we can't answer the question as posed, since you don't show the graphs. But we can help you see what the graph should look like.

The constraints are the the total number of bags is "no more than" 20 and the total cost is "no more than" $140, so both constraint boundary lines are solid.

The constraints are
x%2By%3C=20 --> y%3C=20-x
and
5x%2B14y%3C=140 --> y%3C=10-%285%2F14%29x.

A graph of the constraint boundary lines:

graph%28400%2C400%2C-5%2C20%2C-5%2C20%2C20-x%2C10-%285%2F14%29x%29

Since both constraints are "no more than", which is the same as "less than or equal to", the solution region is on or below both constraint lines -- and obviously only where x and y are both non-negative.

To answer the two specific questions, you can eyeball the graph to see if those combinations are in the feasibility region; but it's much easier (and more accurate) to test the combinations against the constraints.

13 bags of fertilizer and 7 bags of peat moss: the number of bags is no more than 20; but the cost is 13($5)+7($14) = $65+$98 which is more than $140.
ANSWER: NO

14 bags of fertilizer and 4 bags of peat moss: the number of bags is less than 20, and the cost is 14($4)+4($14) = $56+$56 which is less than $140.
ANSWER: YES