The point which provides the solution of the solution to the linear programming problem . Maximum (2x+3y) subject to constraints .
`4x +y ge 4, x +3yge 6,x +y ge 3,x ge 0,y ge 0 ` is

Options

A. (3,2.5)
B. (2.3.5 )
C. (2,3.5)
D. -1.35

Answer

D

Explanation

Feasible regionis OCPQF
Z at 0(0,0)=0+0=0
` therefore Z atC (7/2,0)=2(7/2)+3(0) =7`
`therefore Z at p (5/2 , 2)=2(5/2) +3(2) =11 `
` therefore Z at Q (1,7/2)=2(1)+3(7/2)=(4+21)/(2) = 25/2 ` (Maximum)
Z at F(0,4)=2(0)+3(3)=12
` therefore ` The maximum value of Z=12.5 at (1,3.5)