Question 1191259: Direction: Solve the given problem involving system of linear inequalities by graphing. Andrea does a small business at home. It takes her 2 hours to make a gallon of ice cream (x) and 1 hour for a gallon of concentrated mango juice (y). She can work no more than 10 hours per week. The cost to make a gallon of ice crcam is Php200.00 and the cost to make a concentrated mango juice is Php100.00. She can afford to spend no more than Php2,000.00 per week. Give 3 possible amounts of ice cream and mango juice that Andrea can spend.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! with the desmos.com calculator, you woud do the following:
graph the opposite of the inequalities.
the area on the graph that is not shaded is your region of feasibility.
any coordinate points within the region of feasibility are valid.
since the inequalities are <=, then any values on the lines formed are also valid.
here's what the graph looks like.
3 coordinate points in the region of feasibility have been chosen,.
they are (1,6), (2,4), 3,2).
the coordinate points are in (x,y) format.
for example, the coordinate point of (1,6) means the value of x is 1 and the value of y is 6.
all of the inequalities have to be satisfied at each of the coordinate points.
with (1,6), ....
2x + y <= 10 becomes 2 + 6 <= 10 which becomes 8 <= 10 which is true.
200x + 100y <= 2000 becomes 400 + 100 <= 2000 which becomes 500 <= 2000 which is true.
the controlling factor on the graph is the number of hours.
that's why the region of feasibility is on or below the constraint of 2x + y <= 10
it is possible to satisfy 200x + 100y <= 2000 and not satisfy 2x + y <= 10.
an example is the point (3,8).
200x + 100y = 600 + 800 = 1400 <= 2000.
2x + y = 6 + 8 = 14 which is not <= 10
the coordinate point of (3,8) is not feasible because it does not satisfy all of the constraints, only some.
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