Linear Programming. 20) 3x + y ≤ 7; x + 2y ≤ 9; x ≥ 0; y ≥ 0 Maximize the Objective Function: P = 2x + y show the graph

Answer:The value that maximize the objective function is the point (1,4)Step-by-step explanation:we have[tex]3x+y\leq 7[/tex] ----> inequality A[tex]x+2y\leq 9[/tex] ----> inequality B[tex]x\geq 0[/tex] ----> inequality C[tex]y\geq 0[/tex] ----> inequality DUsing a graphing toolThe solution is the shaded areasee the attached figureThe coordinates of the solution area are[tex](0,0),(0,4.5),(1,4),(2.33,0)[/tex]we haveThe Objective Function is equal to[tex]P=2x+y[/tex]To find out the value of x and y that maximize the objective function, substitute each ordered pair of the vertices in the objective function and then compare the resultsFor (0,0) --------> [tex]P=2(0)+0=0[/tex]For (0,4.5) --------> [tex]P=2(0)+4.5=4.5[/tex]For (1,4) --------> [tex]P=2(1)+4=6[/tex]For (2.33,0) --------> [tex]P=2(2.33)+0=4.66[/tex]The value that maximize the objective function is the point (1,4)