SOLUTION: How do you do this problem? Minimize: Z = 6x+15y Subject to: 4x+5y>=27; 8x+4y>=32; x>=0;y>=0 It's wanting to know the minimum value of Z and what point it occurs at. I can't

Algebra.Com
Question 468927: How do you do this problem?
Minimize: Z = 6x+15y
Subject to: 4x+5y>=27; 8x+4y>=32; x>=0;y>=0
It's wanting to know the minimum value of Z and what point it occurs at.
I can't figure out how to solve this. Thanks.

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Minimize: Z = 6x+15y
Subject to: 4x+5y>=27; 8x+4y>=32; x>=0;y>=0
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Graph each of the restraints:
y >= (-4/5)x + (27/5)
---
y >= -2x +8
---
x >= 0 ; y >=0 means "in the 1st quadrant".
----

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Notice the enclosed area in the 1st quadrant.
---
Find the coordinates of the vertices of the enclosed area:
(0,5.4),(4,0), (2 1/6,3 2/3)
----
Objective Function: Minimize: Z = 6x+15y
----
Evaluate the objective function at each of the
vertex values.
Example:
Using (0,5.4) you would get z = (6*0)+(15*4) = 60
Using (2 1/6, 2 2/3) you would get z = (6*13/6)+15(8/3) = 13+40 = 53
etc.
===============
Cheers,
Stan H.
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