Math Problem Statement
Solution
To make the -10 in the -row a zero using the simplex method, we use the pivot row (the -row here). The correct operation is:
"Multiply the pivot row by 10 and then add it to the row with the -10".
Why?
- The pivot element in the -row for is 1 (highlighted).
- To eliminate in the -row, multiply the pivot row (-row) by 10.
- Add the result to the -row:
.
This operation makes into 0.
Would you like a detailed step-by-step calculation for the row operation? Let me know!
Related Questions:
- What is the pivot element, and how is it chosen in the simplex method?
- Why is the pivot row normalized before elimination?
- How do we determine which column to pivot on in the simplex method?
- What is the difference between the simplex method for maximization and minimization problems?
- How do degeneracy and cycling occur in the simplex method?
Tip:
In the simplex method, row operations aim to eliminate non-zero coefficients in the objective row (top row) while maintaining feasibility in the solution.
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Simplex Method
Pivot Row Operations
Row Operations
Formulas
Row operation: New row = Old row + (Multiplication factor × Pivot row)
Pivot row adjustment: Coefficient elimination
Theorems
Simplex Method for Linear Programming
Suitable Grade Level
Undergraduate (Operations Research or Linear Algebra)