It is given the following transportation problem. I can solve it when the cost is increased, but I don't understand what is the change in the model when the transport cost is reduced.
Problem: It is required to move machines from factories $A, B$ and $C$ to warehouses $X, Y$ and $Z$. There are $5$ required at $X$, $4$ at $Y$ and $3$ at $Z$, whilst there are $8$ available at $A$, $5$ at $B$ and $3$ at $C$. The transport cost in £ between the sites is given in the following table:
Transport cost: $$\begin{array} {|r|r|}\hline & X & Y & Z \\ \hline A & 50 & 60 & 30 \\ \hline B & 60 & 40 & 20 \\ \hline C & 40 & 70 & 30 \\ \hline \end{array}$$
Suppose now there is a reduction in the transport cost of $£10$ per machine taken from A for any machines above six. Find the new optimal solution, but because this time there has been a decrease in price for higher quantity, you will need to solve two problems and also use pricing out.
Thank you for any suggestions.