Question

`{:("Maximize" ,z = 3x + 5y , "subject to "),( ,x + 4y le 24 , 3x + y le 21 "," ),(,x + y le 9 , x ge 0 ", " y ge 0 ):}`

Answer 1

Convert the inequation into equations we have
` x + 4y = 2y, 3x + y = 21 , x + y = 9.`
Scale on both axis 1 cm = 5 units.

Freasible region of LPP is shaded region OABCD.
The vertices of feasible region are O(0,0) A (7, 0),
B(6,3) , C (4,5) and D (0,6).

The value of z is maximum when x = 4 and y = 5 .
`z_("max") = 37`