Assignment:
Q1. Construct the augmented matrix for the following system of three equations in three unknowns. Do not solve the system.
2x – y + z = 10
4x + 2y – 3z = 10
x – 3y + 2z = 8
Q2. Use the Gauss-Jordan method to solve the following system of equations.
5x + 3y = 19
2x – 5y = 11
Q3. Construct the objective function and the system of inequalities for the given situation. Remember to define the variables first. Do not solve the system. Johnson Lumber can convert logs into either lumber or plywood. In a given week, the mill can turn out 400 units of production, of which 100 units of lumber and 150 units of plywood are required by regular customers. The profit on a unit of lumber is $20 and on a unit of plywood is $30.
Q4. Construct the simplex plateau for the objective function and the system of inequalities.
z = 7x + 8y
Subject to
3x + 2y ≤ 12
-x + 2y ≤ 4
x ≥ 0 and y ≥ 0
Q5. Below is the simplex tableau for a linear programming problem.
x y s1 s2 z C
5 3 1 0 0 34
3 5 0 1 0 30
-2 -14 0 0 1 0
a) Identify the pivot column.
b) Determine the pivot and the row in which it occurs.
Provide complete and step by step solution for the question and show calculations and use formulas.