Question 1174699: Mother's weekly budget for fish and chicken is at most Php 1,200. Note that 1 kilogram of fish costs Php
60 while 1 kilogram of chicken costs Php 120.
a. Write a system of inequalities for the given situation then graph the solution set of the system.
b. Determine if the ordered pair (10,7) is a solution to the system.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52858)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your inequality is 60x + 120y <= 1200.
x = the number of kilograms of fish.
y = the number of kilograms of chicken.
two other inequalities that need to be observed are:
x >= 0
y >= 0
when x = 0, the inequality becomes 120y <= 1200.
solve for y to get y <= 1200/120.
simplify that to get:
y <= 10
when y = 0, the inequality becomes 60x <= 1200.
solve for x to get x <= 1200/60.
simplify that to get:
x <= 20
it appears that you have a range of values where the inequality of 60x + 120y <= 1200 is true.
those ranges are:
0 <= x <= 20
0 <= y <= 10
the inequality of 60x + 120y <= 1200 can be graphed.
using the desmos.com calculator, you would graph the inequality of 60x + 120y >= 1200.
you would also graph the inequality of x <= 0 and y <= 0.
all these inequalities being graphed are opposite the inequalities of the problem.
60x + 120y <= 1200 is graphed as 60x + 120y >= 1200
x >= 0 is graphed as x <= 0.
y >= 0 is graphed as y <= 0.
the area on the graph that is not shaded is your region of feasibility.
any value of (x,y) that is on the line of the equation of 60x + 120y = 1200 or on the line x = 0 and between the points (0,0) and (20,0) or on the line
y = 0 and between the points (0,0) and (0,20) or in the area of the graph that is not shaded is a valid point of the system of inequalities.
the graph looks like this.
from the graph, you can see that the point (10,7) is not part of the solution set because it is in the area of the graph that is shaded.
when x = 10 and y = 7, the inequality becomes:
(60 * 10) + (120 * 7) <= 1200 which becomes:
600 + 840 <= 1200 which becomes:
1440 <= 1200 which is not true.
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