WRITE CODE TO SOLVE THE ABOVE LP USING PYTHON

LP Formulation:

Decision Variables:

$$

$1$

$$: Number of chairs produced.

$$

$2$

$$: Number of office tables produced.

$$

$3$

$$: Number of computer tables produced.

$$

$4$

$$: Number of book shelves produced.

Objective Function:

Maximize

$$

$=$

$3$

$5$

$$

$1$

$+$

$3$

$0$

$$

$2$

$+$

$5$

$5$

$$

$3$

$+$

$2$

$0$

$$

$4$

Constraints:

Subject to:

$4$

$$

$1$

$+$

$3$

$$

$2$

$+$

$5$

$$

$3$

$+$

$2$

$$

$4$

$<=$

$1$

$7$

$5$

$0$

$($

$$

$$

$$

$$

$$

$$

$$

$$labor constraint

$)$

$$

$3$

$$

$1$

$+$

$4$

$$

$2$

$+$

$2$

$$

$3$

$+$

$$

$4$

$<=$

$1$

$0$

$0$

$0$

$($

$$

$$

$$

$$

$$

$$

$$

$$

$$labor constraint

$)$

$$

$2$

$$

$1$

$+$

$2$

$$

$2$

$+$

$3$

$$

$3$

$+$

$3$

$$

$4$

$<=$

$1$

$4$

$0$

$0$

$($

$$

$$

$$

$$

$$

$$

$$

$$

$$labor constraint

$)$

$$

$2$

$$

$1$

$+$

$3$

$$

$2$

$+$

$$

$3$

$+$

$2$

$$

$4$

$>=$

$6$

$5$

$0$

$($

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$A contract

$)$

$$

$$

$1$

$+$

$$

$2$

$+$

$2$

$$

$3$

$+$

$$

$4$

$>=$

$4$

$5$

$0$

$($

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$contract

$)$

$$

$$

$1$

$,$

$$

$2$

$,$

$$

$3$

$,$

$$

$4$

$>=$

$0$

$($

$$

$$

$$

$-$

negativity constraints

$)$

$$

The problem is solved using the Big

$-$

M Method

$($

$$

$=$

$1$

$0$

$0$

$)$

$$and the optimal tableau is given below: