Question 1175938: Using the rules of graphing systems of linear equations and inequalities; would you please construct a graph that best shows the area of each crop that can be planted?
A farm has an area of 50 Hectares (Ha). It is to be planted with tomatoes and potatoes. At most $8000 can be spent on planting. The planting cost for potatoes is $100/Ha and for tomatoes $200/Ha. Choose the graph that best shows the area of each crop that can be planted.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the two inequalities that need to be satisfied simultaneously are:
x + y <= 50
100x + 200y <= 8000
using the desmos.com calculator, you would graph the opposite of these inequalities.
the area on the graph that is not shaded is the feasible region.
the feasible region includes any point on the graph that lies on the line x = 0, y = 0, x + y = 50, and 100x + 200y = 8000, as well as in the unshaded ara of the graph, because the inequalities are inclusive of the points on those lines, i.e. they are <= rather than <, and >= rather than >.
your graph will look something like this.
the points in red are outside the feasible region.
they do not satisfy all the constraints.
the points in black are inside the feasible region.
they do satisfy all the constraints.
for example:
the point (20,30) is in the feasible region.
it satisfies the constraint functions.
the point (40,30) is not in the feasible region.
it does not satisfy the constraint functions.
the constraint functions are:
x + y <= 50
100x + 200y <= 8000
at the point (20,30), x + y = 30 which is <= 30 and 100x + 200y = 8000 which is <= 8000.
that point is in the f3easible region and satisfies all the constraints.
at the point (40,30), x + y = 70 which is not <= 50 and 100x + 200y = 10,000 which is not <= 8000.
that point is not in the feasible region and does not satisfy all the constraints.
note that all the constraints need to be satisfied. failure to satisfy any one of the constraint is enough to make the point not feasible.
for example, the point (50,10) gives you the following results.
x + y = 60 which is not <= 50 and so it does not satisfy the x + y <= 50 constraint.
100x + 200y = 7000 which is <= 8000 and so it does satisfy the 100x + 200y <= 8000 constraint.
since the point (30,10) doesn't satisfy all of the constrains it is not in the feasible region.
this can be seen on the graph because it is in the shaded region.
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