@abie232t Dm

1.To form the initial simplex tableau, we need to introduce slack variables and set up the problem in standard form. The standard form of the given linear programming problem is: Maximize Z = 10X1 + 8X2 + 0S1 + 0S2 + 0S3 Subject to: X1 + X2 + S1 = 50 2X1 + 4X2 + S2 = 400 3X1 + 5X2 + S3 = 300 Where S1, S2, S3 are slack variables. Now, we can form the initial simplex tableau as follows: | BV | X1 | X2 | S1 | S2 | S3 | RHS | |----|----|----|-----|-----|-----|-----| | S1 | 1 | 1 | 1 | 0 | 0 | 50 | | S2 | 2 | 4 | 0 | 1 | 0 | 400 | | S3 | 3 | 5 | 0 | 0 | 1 | 300 | | Z | -10| -8 | 0 | 0 | 0 | 0 | Where BV represents Basic Variables and the coefficients of the decision variables X1 and X2, slack variables S1, S2, and S3, and the objective function Z are arranged in a table. The RHS column represents the amounts on the right-hand side of the constraints. The initial basic variables are S1, S2, and S3, and Z is equal to zero.

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