Verified Answer :

HomertheGenius

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

calculista

Let

A--------> the corner point in the graph \((0,0)\)

B--------> the corner point in the graph \((0,8)\)

C--------> the corner point in the graph \((6,5)\)

D--------> the corner point in the graph \((8,0)\)

we know that

The function P is equal to

\(P=2x+3y\)

Step \(1\)

Evaluate the function P in each corner point

point \(A(0,0)\)

\(x=0\\ y=0\\ PA=2*0+3*0\\ PA=0\)

point \(B(0,8)\)

\(x=0\\ y=8\\ PB=2*0+3*8\\ PB=24\)

point \(C(6,5)\)

\(x=6\\ y=5\\ PC=2*6+3*5\\ PC=27\)

point \(D(8,0)\)

\(x=8\\ y=0\\ PD=2*8+3*0\\ PD=16\)

the maximum value of P is for the point C

\(PC=27\)

therefore

the answer is

The maximum value of the function P is \(27\)

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