Expert: David Hemmer - 12/30/2010

Question
Hi.
Having trouble solving the following problem. I'm a degree student working on a concept from an economist called Scott Barrett. Part of this involves some equations. I've simplified the two inequalities to:

3.5>j+0.5k>0.5 and j+2k>5

How would I go about solving these to find values for j and k?
I've never had to solve an inequality like that, and assume I should do it simultaneously!
Thanks

Answer
The easiest way is to look at the equalities:

j+.5k=3.5
j+.5k=.5

These are two parallel lines in the j-k plane. So the first pair of inequalities says your the (j,k) will like between these two parallel lines (but not include them).

Now the third line j+2k=5 will cut across this region and j+2k>5 will be one side of the line.

So your solutions will be an infinite strip in one direction with a triangle on one side, shape like below. There's not necessarily any nice way to write the answer.
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