Minimum and Maximim Values of a Funtion?

[QHansen]

Doing a unit on linear programming in Algebra 2, and I have no idea where to start with a lot of these problems. Question reads:

Given the objective funtion P and the constraints, find the minimum and maximum values for the objective function.

P = 2x + 3y given x (greater than or equal to) 0, y (greater than or equal to) 0, 0.4x + 0.9y (less than or equal to) 25

Thanks for any help, I have no idea how to approach this problem. Made an account on here just for these, haha.

 

[Otis]

Doing a unit … I have no idea …

I'm not sure that I understand. It sounds like your unit has not provided any instruction.

Let's get you some lessons. Google the phrase linear programming. The linear programming method (i.e., graphing lines using xy-coordinates to create an enclosed region, finding the coordinates at each vertex, and testing them for P) is explained in videos and in written lessons, at many web sites. Once you've studied the method and worked some examples, try your exercise. If you see something you don't understand, ask us about it; otherwise, show us how far you got, in your exercise. Cheers :cool:

PS: Here's a link to the forum's submission guidelines.

 

[JeffM]

Doing a unit on linear programming in Algebra 2, and I have no idea where to start with a lot of these problems. Question reads:

Given the objective funtion P and the constraints, find the minimum and maximum values for the objective function.

P = 2x + 3y given x (greater than or equal to) 0, y (greater than or equal to) 0, 0.4x + 0.9y (less than or equal to) 25

Thanks for any help, I have no idea how to approach this problem. Made an account on here just for these, haha.

Do you see that P can be driven to any height whatsoever by increasing x, y, or both in the positive direction? Do you see that P can be driven to any depth whatsoever by "increasing" x, y, or both in the negative direction.

If there are limits on x and y separately or jointly, then P will have a minimum and a maximum value that is consistent with all those constraints. Do you see why that is so?

For very simple problems of this type, you can find the maximum and minimum by doing some graphing and a small number of computations. Otis has given you suggestions on where to find lessons on how to solve these very simple problems.

I must admit I do not see why the schools are now presenting these very simple linear programming problems. The technique taught does not expand to more complicated problems. However, such problems do provide exercise in graphing inequalities. Perhaps that is the point.

 

[Denis]

Given the objective funtion P and the constraints, find the minimum and maximum values for the objective function.

P = 2x + 3y given x (greater than or equal to) 0, y (greater than or equal to) 0, 0.4x + 0.9y (less than or equal to) 25

Since x => 0 and y =>0, and P = 2x + 3y,
then minimum P is automatically 0.
So you only need maximum P, right?
Or did I miss something?

 

[Steven G]

Doing a unit on linear programming in Algebra 2, and I have no idea where to start with a lot of these problems. Question reads:

Given the objective funtion P and the constraints, find the minimum and maximum values for the objective function.

P = 2x + 3y given x (greater than or equal to) 0, y (greater than or equal to) 0, 0.4x + 0.9y (less than or equal to) 25

Thanks for any help, I have no idea how to approach this problem. Made an account on here just for these, haha.

The max will occur at a corner point. Draw x>0, y>0 and 4x+9y < 250. The 1st two are just the x and y axes. This will give you a triangular region which has 3 corner points. Compute the value for P at each corner point. Which ever is largest will be the max of P. Clearly (0,0) is where the min occurs. Do you see that?