In the code below i recieved Run Time Error $\text{'}13\text{'}-$ Type Missmatch. I have attached a screen shot showing where the Debugger shows the error is located. Can you please help me with this code. ThanksDim pivotValue As DoublenumCols $=$ tableau.Columns.Count' Divide the pivot row by the pivot element tableau.Cells$($pivotRow$,$ j$).$Value $=$ tableau.Cells$($pivotRow$,$ j$).$Value $/$ pivotValue' Subtract multiples of the pivot row from the other rows If i pivotRow Then For j $=1$ To numCols Next jNext i

End Sub

Option Explicit

Sub SimplexMethod$()$

Dim tableau As Range

Dim numRows As Integer, numCols As Integer

Dim pivotRow As Integer, pivotCol As Integer

Dim i As Integer, j As Integer

Dim minRatio As Double, ratio As Double

$\text{'}$ Define the range of the initial tableau

Set tableau $=$ ThisWorkbook.Sheets$("$Simplex$").$Range$("$A$2$:D$5")$

numRows $=$ tableau.Rows.Count

numCols $=$ tableau.Columns.Count

Do

$\text{'}$ Step $1$: Identify the pivot column $($most negative value in the objective row$)$

pivotCol $=1$

For j $=2$ To numCols $-1$

If tableau.Cells$($numRows$,$ j$).$Value $$ tableau.Cells$($numRows$,$ pivotCol$).$Value Then

pivotCol $=$ j

End If

Next j

$\text{'}$ If all values in the objective row are non$-$negative, the solution is optimal

If tableau.Cells$($numRows$,$ pivotCol$).$Value $>=0$ Then Exit Do

$\text{'}$ Step $2$: Identify the pivot row $($minimum positive ratio of RHS to pivot column$)$

minRatio $=1$E$+30$

For i $=1$ To numRows $-1$

If tableau.Cells$($i$,$ pivotCol$).$Value $>0$ Then

ratio $=$ tableau.Cells$($i$,$ numCols$).$Value $/$ tableau.Cells$($i$,$ pivotCol$).$Value

If ratio $$ minRatio Then

minRatio $=$ ratio

pivotRow $=$ i

End If

End If

Next i

$\text{'}$ Step $3$: Perform pivot operation

Pivot tableau, pivotRow, pivotCol

Loop

$\text{'}$ Output the optimal solution

MsgBox "Optimal solution found. Objective value: $"$ & tableau.Cells$($numRows$,$ numCols$).$Value

End Sub

Sub Pivot$($tableau As Range, pivotRow As Integer, pivotCol As Integer$)$

Dim numRows As Integer, numCols As Integer

Dim i As Integer, j As Integer

Dim pivotValue As Double

numRows $=$ tableau.Rows.Count

numCols $=$ tableau.Columns.Count

pivotValue $=$ tableau.Cells$($pivotRow$,$ pivotCol$).$Value

$\text{'}$ Divide the pivot row by the pivot element

For j $=1$ To numCols

tableau.Cells$($pivotRow$,$ j$).$Value $=$ tableau.Cells$($pivotRow$,$ j$).$Value $/$ pivotValue

Next j

$\text{'}$ Subtract multiples of the pivot row from the other rows

For i $=1$ To numRows

If i pivotRow Then

pivotValue $=$ tableau.Cells$($i$,$ pivotCol$).$Value

For j $=1$ To numCols

tableau.Cells$($i$,$ j$).$Value $=$ tableau.Cells$($i$,$ j$).$Value $-$ pivotValue $*$ tableau.Cells$($pivotRow$,$ j$).$Value

Next j

End If

Next i

End Sub