(Solved): question (b) 3. Sunflower Furniture Company manufactures three types of tables with different quali ...

question (b)

3. Sunflower Furniture Company manufactures three types of tables with different quality: low, moderate and high quality. Each type of the production requires the use of machines A, B and C. The machine hours required to produce each type of table and the selling price (RM) per unit for different types of table are given in the following table: By letting \( x_{1}, x_{2} \) and \( x_{3} \) be the number of units of low quality table, moderate quality table and high quality table produced, respectively. Then the linear programming model becomes: Maximize \( z=200 x_{1}+300 x_{2}+400 x_{3} \) subject to \[ \begin{array}{l} 2 x_{1}+3 x_{2}+x_{3} \leq 20 \\ 2 x_{1}+3 x_{2}+2 x_{3} \leq 18 \\ 2 x_{1}+x_{2}+4 x_{3} \leq 16 \\ x_{1}, x_{2}, x_{3} \geq 0 \end{array} \] The slacks \( x_{4}, x_{5} \) and \( x_{6} \) are added to the model. The linear programming model yields the following optimal simplex tableau: (b) Find the dual model for the given linear programming model.