Question

Using Simplex method
Maximize Z = 5x1+3x2
Subject to x1+x2 ≤ 2
5x1+2x2 ≤ 10
3x1+8x2 ≤ 12
x1, x2 0

Answer 1

Answer:

hmmm .

Step-by-step explanation:

Using Simplex method

Maximize Z = 5x1+3x2

Subject to x1+x2 ≤ 2

5x1+2x2 ≤ 10

3x1+8x2 ≤ 12

x1, x2 0

Answer 2

Max Z = 10

Given:

Max Z =5x1 + 3x2

STC

x1 + x2 <= 2

5x1 + 2x2 <= 10

3x1 + 8x2 <= 12

x1, x2 >= 0

To find:

Max Z

Solution:

Step 1: Since the problem is maximization problem all the constraint are <= type and the

requirements are +ve. This satisfies the simplex method procedure.

Step 2: since all the constraints are <= type we introduce the slack variables for all the

constraints as x3 >=0, x4 >=0, x5 >=0 for the I II and III constraint

Step 3: the given LPP can be put in standard form

Max Z =5x1 + 3x2 + (0) x3+ (0) x4 + (0)x5

STC

x1 + x2 + x3 <= 2

5x1 + 2x2+ x4 <= 10

3x1 + 8x2 + x5 <= 12

x1, x2 ,x3,x4 ,x5 >= 0

Step 4: matrix form

Max Z = (5,3,0,0,0) (x1, x2 ,x3,x4 ,x5 )

Since, the given problems net evaluation row is +ve, then given problem as attained the

optimum

Therefore, x1 =2, x2 =0, x3 =0, x4 =0, x5 =6,

Substitute in the objective function

Max Z =5x1 + 3x2 + (0) x3+ (0) x4 + (0)x5

Max Z =5x2+3x0+0x0+0x0+0x6

Max Z = 10

Hence, Max Z=10.

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