Find the Maximum Value
Algebra
Level
2
Find the maximum value of 5X + 4Y such that
2X + 3Y <= 7
and
2X - Y <= 2
and
X,Y are >= 0.
13.125
0
9.333
5
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1 solution
These two equations
2X + 3Y <= 7
2X - Y <= 2 can be graphically represented as
The maximum or minimum value of 5X + 4Y will fall on the vertices of the feasible region A, B , C or D as ABCD is a convex polytope.
So calculating the value of 5X + 4Y at A, B, C and D respectively yields a maximum value of 13.125 at Point C. The above is an example of a Linear Programming Problem ,simple formulations of which can be solved graphically. Linear Programming .
It can also be verified randomly that any point inside the polytope ABCD such as (1,1) will yield a smaller value of the objective function than the maximum or extreme value which will fall on the vertex. In fact the minimum value of 5X + 4Y (objective function) will fall on another vertex A. Value 0.