Questions on Algebra: Matrices, determinant, Cramer rule answered by real tutors!

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Question 163622This question is from textbook College Algebra
: Find the maximum value of F=7y-4x subjet to
x+y 4x-3y x>or=0
y>or=0This question is from textbook College Algebra
: Find the maximum value of F=7y-4x subjet to
x+y 4x-3y x>or=0
y>or=0
Answer by Fombitz(1789) About Me  (Show Source):
You can put this solution on YOUR website!
First let's graph the feasible region.
x+y<=8
4x-3y<=12
x>=0
y>=0
graph( 300, 300, -2, 10, -2, 5, 8-x, (4x-12))
The feasible region is the triangle bounded by vertices (3,0),(8,0), and (36/7,20/7).
The final point is determined by equating
y=8-x
and
y=(4x-12)/3
as shown here,
8-x=(4x-12)/3
24-3x=4x-12
-7x=-36
x=36/7
Then
y=8-x
y=8-36/7
y=56/7-36/7
y=20/7
.
.
.
The max and min of F occur at the vertices of the feasible region.
Check all the points to determine.
.
.
.
(3,0)
F=7y-4x
F=7(0)-4(3)
F=-12
.
.
.
(8,0)
F=7y-4x
F=7(0)-4(8)
F=-32
.
.
.
(36/7,20/7)
F=7y-4x
F=7(20/7)-4(36/7)
F=140/7-144/7
F=-4/7
.
.
.
The min value occurs at (8,0) where F=-32.