Answer:
The maximum value of Z is 2,000 for x_1=10 and x_2=0
Step-by-step explanation:
we have
[tex]8x_1+5x_2\leq 80[/tex] -----> inequality A
[tex]2x_1+x_2\leq 100[/tex] -----> inequality B
[tex]x_1\geq 0[/tex] -----> inequality C
[tex]x_2\geq 0[/tex] -----> inequality D
Solve the system of inequalities by graphing
The solution is the triangular shaded area
see the attached figure
The vertices of the shaded area are
(0,0),(0,16) and (10,0)
we have
[tex]Z=200x_1+100x_2[/tex]
To find out the maximum value of Z, substitute the value of x_1 and the value of x_2 of each vertex and then compare the results
[tex]For\ (0,0) ----> Z=200(0)+100(0)=0[/tex]
[tex]For\ (0,16) ----> Z=200(0)+100(16)=1,600[/tex]
[tex]For\ (10,0) ----> Z=200(10)+100(0)=2,000[/tex]
therefore
The maximum value of Z is 2,000 for x_1=10 and x_2=0
