Answer:
The maximum value of z is 244 at x= 8 and y=49.
Step-by-step explanation:
We are given the system of equations as,
Maximize : [tex]z= 6x+4y[/tex]
Subject to : [tex]8x-y\leq 15[/tex]
[tex]3x + y\geq 10[/tex]
[tex]x\geq 2[/tex]
[tex]x\leq 8[/tex]
After plotting the inequalities to which the maximized function is subjected to, we get the following graph.
So, we will find the value of 'z' at the enclosing the solution region.
[tex]z= 6x+4y[/tex]
(2,4) z= 6×2+4×4= 12+16 = 28
(2.273,3.182) z= 6×2.273+4×3.182 = 13.64+12.73= 26.37
(8,49) z= 6×8+4×49 = 48+196= 244
Thus, we get that the maximum value of z is 244 at x= 8 and y=49.
