By graphical method, the solutions of linear programming problem maximum ` Z = 3x_1 + 5x_2` subject to constraints `3x_1+2x_2 le 18`
`x_1 le 4, x_2 le 6,x_1 ge 0, x_2 ge 0`

Options

A. ` x_1=2, x_2 =6, Z =36 `
B. `x_1=2, x_2=6 , Z=36 `
C. ` x_1=4,x_2 =3, Z=27 `
D. `x_1=4, x_2=6,Z=42 `

Answer

B

Explanation

The feasible region is OABCDO, whose corner points are O (0, 0), A ( 4, O), B ( 4, 3), C (2, 6) and D (0, 6). :. Table for objective function is given as: ` therefore ` Table for objective function is given as:

Hence, maximum values of Z is 36 at point C(2, 6). So, `x_1 =2, x_ 2` =6andZ=36