SOLUTION: For values of x and y defined by the region defined by the inequalities 2x+y>120, y>x and y<2x, find the minimum value of V when V=5x+4y-100. Thank you :D

Algebra ->  Linear-equations -> SOLUTION: For values of x and y defined by the region defined by the inequalities 2x+y>120, y>x and y<2x, find the minimum value of V when V=5x+4y-100. Thank you :D      Log On


   

Question 1130500: For values of x and y defined by the region defined by the inequalities 2x+y>120, y>x and y<2x, find the minimum value of V when V=5x+4y-100. Thank you :D
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
The region of the interest is shown in the plot below.

It is infinite area in the first quadrant, bounded by the 3 straight lines: red, green and blue.



graph%28+330%2C+330%2C+-10%2C+80%2C+-10%2C+150%2C%0D%0A++++++++++120-2x%2C+x%2C+2x%0D%0A%29


Plot  2x+y = 120 (red),  y = x (green) and y = 2x (blue)


To find the minimum of the given function V(x,y) = 5x + 4y - 100,  you need to calculate its values in the corner point of the gerion
and the choose that corner point where the value of the function is minimal.


The corner points are  P1 = (40,40)   and  P = (30,60).


The values of the function V are:  at P1  V = 5*40 + 4*40 - 100 = 260   and
                                   at P2  V = 5*30 + 4*60 - 100 = 290.


The minimum value of V over the region is 260; it is achieved at the point P1.

Solved.

To see many other similar problems solved by the Linear Programming method,  look into the lesson
    - Solving minimax problems by the Linear Programming method
in this site.