Solving Linear Inequalities on a TI-83 Calculator

In summary, to minimize and maximize the linear equation P=30x+10y subject to given inequalities, one must plot the 5 lines representing the constraints and find the feasible region bounded by those lines. Then, by finding the points of intersection and evaluating the linear equation at those points, the minimum and maximum values of P can be determined. It is not possible to graph the inequalities on a calculator, but one can graph the corresponding equations and manually determine the feasible region.
  • #1
Corkery
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Homework Statement


Mnimize and maximize:
P=30x + 10y
Subject to 2x + 2y > or = 4
6x + 4y < or = 36
2x + y < or = 10
x, y > or = 0

Homework Equations


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.
 
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  • #2
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
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
What, do it the "old fashioned way? How primitive!

Of course, if it easier to do it by hand than with a calculator...
 
  • #5
HallsofIvy said:
You CAN'T graph an inequality on a calculator.

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

FAQ: Solving Linear Inequalities on a TI-83 Calculator

1. How do I enter linear inequalities on a TI-83 calculator?

To enter a linear inequality on a TI-83 calculator, you will need to use the "inequality" function. Press the "Y=" button and then use the right arrow key to navigate to the "inequality" function. From there, you can enter the variables, operators, and constants for your inequality. Make sure to use the correct symbols for "less than" (<) and "greater than" (>) when entering your inequality.

2. How do I graph linear inequalities on a TI-83 calculator?

To graph a linear inequality on a TI-83 calculator, you can use the "inequality" function in the same way as mentioned above. Once the inequality is entered, press the "graph" button to see the graph of the inequality. You may need to adjust the window settings to see the full graph.

3. Can I solve systems of linear inequalities on a TI-83 calculator?

Yes, you can solve systems of linear inequalities on a TI-83 calculator by using the "inequality" function to enter each inequality in the system. Then, press the "graph" button to see the solution region for the system. You can also use the "intersect" function to find the coordinates of any points where the inequalities intersect.

4. How do I check the solution to a linear inequality on a TI-83 calculator?

To check the solution to a linear inequality on a TI-83 calculator, you can use the "value" function. First, enter the inequality into the "Y=" menu. Then, press the "value" button and enter a value for the variable in the inequality. If the value is true, it will display "1" and if it is false, it will display "0". This can help you check if a certain point is a solution to the inequality.

5. Can I use a TI-83 calculator to solve quadratic inequalities?

Yes, you can use a TI-83 calculator to solve quadratic inequalities by using the "inequality" function to enter the quadratic inequality. Then, you can use the "intersect" function to find any points where the inequality intersects with the x-axis. These points can help you determine the solution region for the inequality.

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