SOLUTION: Please solve the following linear programming problem. maximize :z=4x+2y subject to: 7x-4y<=14 2x+y=>10 x=>2 y<=8 The maximum value is___

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please solve the following linear programming problem. maximize :z=4x+2y subject to: 7x-4y<=14 2x+y=>10 x=>2 y<=8 The maximum value is___       Log On


   



Question 1098380: Please solve the following linear programming problem.
maximize :z=4x+2y
subject to: 7x-4y<=14
2x+y=>10
x=>2
y<=8
The maximum value is___
The maximum occurs at what points ___

Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graphing the feasible region, two points are clear, the other two you need to solve for.
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7x-4%288%29=14
7x-32=14
7x=46
x=46%2F7
(46%2F7,8)
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Next solve for the intersection of the two lines,
7x-4y=14
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2x%2By=10
8x%2B4y=40
Adding to the first equation,
7x-4y%2B8x%2B4y=14%2B40
15x=54
x=54%2F15
So then,
2%2854%2F15%29%2By=150%2F15
108%2F15%2By=150%2F15
y=42%2F15
(54%2F15,42%2F15)
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Now check the value of the function at each of the vertices.
I'll do one, you do the other three the same way.
(2,6)
z=4x%2B2y
z%282%2C6%29=4%282%29%2B2%286%29=8%2B12=20
Do the others exactly the same way.

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
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On solving linear programming problems,  see the lesson
    - Solving minimax problems by the Linear Programming method
in this site.