For the feasibility region shown below, find the maximum value of the function P=2x+3y.

Corner points in this graph are: ( 0,0 ) ( 0,8 ) ( 5,6 ) and ( 8, 0 ).
If we plug those values in : P = 2 x + 3 y
P ( 0,0 )= 0
P ( 0,8 ) = 2 * 0 + 3 * 8 = 24
P ( 6 , 5 ) = 2 * 6 + 3 * 5 = 12 + 15 = 27
P ( 8 , 0 ) = 2 * 8 + 3 * 0 = 16
The maximum value is:
P max ( 6 , 5 ) = 27

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calculista calculista · Answer 2 · 2018-08-13T00:03:42+02:00

Let

A--------> the corner point in the graph [tex] (0,0) [/tex]

B--------> the corner point in the graph [tex] (0,8) [/tex]

C--------> the corner point in the graph [tex] (6,5) [/tex]

D--------> the corner point in the graph [tex] (8,0) [/tex]

we know that

The function P is equal to

[tex] P=2x+3y [/tex]

Step [tex] 1 [/tex]

Evaluate the function P in each corner point

point [tex] A(0,0) [/tex]

[tex] x=0\\ y=0\\ PA=2*0+3*0\\ PA=0 [/tex]

point [tex] B(0,8) [/tex]

[tex] x=0\\ y=8\\ PB=2*0+3*8\\ PB=24 [/tex]

point [tex] C(6,5) [/tex]

[tex] x=6\\ y=5\\ PC=2*6+3*5\\ PC=27 [/tex]

point [tex] D(8,0) [/tex]

[tex] x=8\\ y=0\\ PD=2*8+3*0\\ PD=16 [/tex]

the maximum value of P is for the point C

[tex] PC=27 [/tex]

therefore

the answer is

The maximum value of the function P is [tex] 27 [/tex]