Hi Karen,
The first inequality is just two vertical lines, one at x=30 and the other at x=80 any x in-between those lines is a solution.
The second inequality is incorrect, there should be a variable (either x or y) somewhere in the relationship.
If it is a y then the graph would be two horizontal lines one at y=30 and one at y=10. If you combine the two inequalities it describes a rectangle in the x,y plane with corners at (30,10) (30,30) (80,10) (80,30)
Hope this helps
Jim
Karen L.
Since you were so helpful..i am doing objective functions...word problems..got that down,got the "constraints" now they need to be graphed...
so i have: x<=6 which i know to make x=6 and its a vertical line at 6.
next one is y>=1 which i change to y=1 and know that its a horizontal line at 1
the last one is 2x-y>=-1 i solve for x first 2x- 0 =-1 or x=-1 (-1,0) then -y=-1 or y=1 (0,1) so these are all my points to plot..the text book gives an answer that makes no sense...they have coordinates of (6,1) (0,1) and (6,13) huh?
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06/09/14
Jim S.
tutor
Hi Karen, I guessed right….glad I cold help. As for the new problem you are correct for x=6 and y=1. The third part 2x-y>=-1 is a straight line y=2x+1. To find the solution region you want to find out where the line y=2x+1 intersects the horizontal
(y=1) and vertical (x=6). This is most easily found by graphing x=6 y=1 and y=2x+1. The region enclosed is bounded by a right triangle. So you are looking for three sets of coordinates which are the vertices of the triangle.
- when x=6 y=2*6+1=13 so one corner is (6,13)
- when y=1 x=1/2*(y-1)=1/2*0=0 so the other corner is (0,1)
- when y=1 x=6 is the third corner (the right angled corner) (6,1)
Let me know if you have any other questions
Jim
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06/09/14
Karen L.
yes,linear programming...new subject in class..
on 2x-y>=-1 why isnt it the same way as the other two problems...solving for x and then for y?and why is it y=2x+1 not -1? i n eed more explanation on that...i
so the first two are related to the last one? I was trying to solve them all seperately..thats where i am stuck
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06/09/14
Jim S.
tutor
Karen,
First 2x-y>=-1 if you put this equation in y=mx+b form, i.e. solve for y in terms of x as follows
2x-y=-1 subtract 2x form both sides
-y=-1-2x multiply both sides by -1
y=2x+1 is the equation of a line with slope, m=2 and intercept, b=1
this is the equation of one of the boundaries.
The other two are x=6 and y=1 these are special lines (vertical, infinite slope and horizontal, zero slope)
If you graph the three lines you will see the solution region, a right triangle
Jim
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06/09/14
Karen L.
06/09/14