Linear inequalities

1. Nov 28, 2007

Corkery

1. The problem statement, all variables and given/known data
Mnimize and maximize:
P=30x + 10y
Subject to 2x + 2y > or = 4
6x + 4y < or = 36
2x + y < or = 10
x, y > or = 0

2. Relevant equations

3. The attempt at a solution

How would I go about graphing this on my calculator: 2x + 2y > or = 4. When I take out my ti-83 and try to input the equation 2x + 2y > or = 4 I can't seem to find how to put multiple variables into it and inout less than or equal to signs in there. I do realize how to do this pblem I just can't seem to grasp the idea of how to put it into a calculator. I would greatly appreciate all your help you can provide. Thanks.

2. Nov 29, 2007

HallsofIvy

Staff Emeritus
You CAN'T graph an inequality on a calculator. You can, however, graph the equation 2x+ 2y= 4 (solve for y and enter it as y= 2- x) and that is the boundary between "> 4" and "< 4". Since you have 5 inequalities, your "feasible" region will be the five sided figure bounded by those 5 lines. I'm sure that you know that the minimal and maximal values of your linear target function will occur at one of the 5 vertices of that region.

3. Nov 30, 2007

qspeechc

Why use a calculator? Why not do it by hand? Don't be lazy! As HallsofIvy says, the 'feasible' region- the region that satisfies all inequalities- is the region bounded by all 5 lines. So plot the 5 lines by hand and find the bounded region. Then find all the points of intersection, see which point gives the lowest value for P= 30x + 10y- this will the minimisation of P, and the point that gives the highest value will be the maximum.

4. Nov 30, 2007

HallsofIvy

Staff Emeritus
What, do it the "old fashioned way? How primitive!

Of course, if it easier to do it by hand than with a calculator...

5. Dec 1, 2007

Xorlev

You can, but you have to choose the shaded area for yourself. Much easier to do so manually.