Question 1207236: The following constraints are given for a linear programming problem
y + 2x>8
3y +2x>18
y<2x
x>1
1. Sketch the graph with the given constraints.
2. Shade the feasible region on the graph.
3. Find the values of x and y that will maximize the profit if the objective function is P= x + y.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
The following constraints are given for a linear programming problem
y + 2x>8
3y +2x>18
y<2x
x>1
1. Sketch the graph with the given constraints.
2. Shade the feasible region on the graph.
3. Find the values of x and y that will maximize the profit if the objective function is P= x + y.
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As presented in this post, the given objective function has no maximum; so the posed problem has no solution.
Indeed, it is clear that under given constraints the feasibility domain is the area
unbounded from the side of great positive x and y; that allows the objective function
P = x + y to grow unlimited.
Thus, the problem is posed INCORRECTLY and HAS NO solution.
So, either a person who created this " problem ", is mathematically illiterate in the subject,
OR this person is extremely inaccurate, OR the problem is extracted from an untrusted source without thinking
in the hope that there will be a qualified reader who will find and note an error.
Here " OR " is not exclusive: these listed rationalities may come together in different combinations.
It is what usually happens at this forum every day, and even several times per day.
Therefore, this cleaning, which I make at this forum daily/regularly, is absolutely necessary
and deserves the greatest gratitude from visitors.
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