Asked by Sam

Which term best describes the solution of the situation represented by the system of inequalities? (Assume that x >= 0 and y >= 0.)
3x + 4y <= 8
2x + 4y <= 6

Answer choices given are:
a. alternate optimal solutions
b. one optimal solution
c. unbounded
d. infeasible

I have no clue how to do this and what they are asking for. (I can't seem to find any video covering this in Khan Academy either.)

Answers

Answered by Steve
Consider each line as if it were an equation. For example,

3x+4y = 8

That describes a line in the x-y plane. But, you have an inequality. So, the solution is the entire half-plane below the line, where 3x+4y <= 8

Same for the other inequality.

So, the solution set for the system is the intersection of those two regions: the entire plane which is below both lines.

See the solution at

http://www.wolframalpha.com/input/?i=solve+3x+%2B+4y+%3C%3D+8%2C+2x+%2B+4y+%3C%3D+6
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