Finite Math Questions

[eldoradoescobar]

Looking for help on any of these questions thanks......

 

[mmm4444bot]

Hello. These appear to be linear-programming type exercises. Have you studied linear programming? What is your math class currently doing?

The freemathhelp boards are for tutoring. (We do not teach course material here).

Please explain what you've tried or thought about, thus far. Only then will we be in a position to determine where to begin helping you.

(We ask that people not post lists of exercises with no work shown or questions asked. Additional information may be found in our Forum Guidelines. For future reference, we also prefer to discuss only one exercise per thread. In the future, please begin a new thread for each new exercise.)

If you cannot make any start at all, then start with these Google search results. That is, seek out information about linear programming. Please feel free to ask specific questions about anything that confuses you, in your studies.

Cheers :cool:

 

[eldoradoescobar]

Sorry first timer here....

I've gotten pretty far on the problems. I was able to set the problem up on a table, put the information into equations and then I was able to graph the equations..... Where I get confused is what part of the graph to shade and how to get the points to the unknown intersecting points..... I included where I got on problem #1 (i guessed where to shade at) and not sure how to figure the unknown x,y intercept....

 

[mmm4444bot]

I was able to graph the equations.

Where I get confused is what part of the graph to shade and how to get the [coordinates of] the unknown intersecting [point]

It looks like you set up the system of inequalities correctly.

Your graph looks good, too, with one exception; do not extend the lines outside of Quadrant I.

Any point on either line that lies outside Quadrant I must have either a negative x-coordinate OR a negative y-coordinate. (There are no negative numbers of either rats or mice, in this exercise.)

Hence, you should also state the following inequalities:

x ≥ 0

y ≥ 0


It will also help other people looking at your work to understand your reasoning, if you state the definitions for symbols x and y as your very first step:

x = the number of mice used per day

y = the number of rats used per day

Then use x and y throughout (do not use m and r simultaneously -- too many symbols).


You shaded the correct region. Only points on the solid lines or in that shaded region have (x,y) values that satisfy BOTH of your posted inequalities. Any other point is not part of the system's solution.


To find the intersection point, you could first solve each equation for y and equate the results. (Before solving for y, I suggest dividing both sides of each equation by 10 to reduce the numbers.)

After you equate the results for y, you'll have an equation that contains only the symbol x. Solve that equation for x.

Use the x-solution to calculate the corresponding y-coordinate (you may use one of the equations that you solved for y, to do this.)


EG:

5x + 4y = 1050

4x + 8y = 1200

Solve each for y:

y = (-5x + 1050)/4

y = (-4x + 1200)/8 = (-x + 300)/2

Equate the results to form an equation that contains only x:

(-5x + 1050)/4 = (-x + 300)/2


Give this method a try, and let us know if you get stuck.

Cheers :cool:

 

[mmm4444bot]

Oh, I forgot.

What is your objective function?

That is, what expression involving x and y are you trying to maximize?

Do you know? The vertex coordinates of the shaded region provide the four sets of (x,y) values that you need to test.