Question $4)$ Degirmenogullari A$..$ produces flour at their five plants. The capacity $($in tons$)$ of each plant $($P$)$ is given below.

P$1$ P$2$ P$3$ P$4$ P$5300200300200400$

The flour produced in these plants is stored at one of three warehouses. The cost $($in hundreds of TLs$)$ of shipping a ton of flour from each plant $($P$)$ to each warehouse $($W$)$ is as follows.

W$1$ W$2$ W$3$

P$181012$

P$2757$

P$3865$

P$4567$

P$5765$

Four retail store chains are the customers $($C$)$ of Degirmenogullari. The demand for each customer $($in tons$)$ is given below.

C$1$ C$2$ C$3$ C$4200300150250$

The cost of shipping a ton of flour from each warehouse to each customer is as given below. C$1$ C$2$ C$3$ C$4$

W$140$ W$270$ W$380$

$809050706080305060$

a$)$ Formulate a model for Degirmenogullari A$..$ to minimize the cost of satisfying demand. Solve it using Excel.

b$)$ Modify this problem if there is a fixed annual cost of operating each plant and warehouse. These costs $($in thousands$)$ are given below. Solve it using Excel.

P$1$ P$2$ P$3$ P$4$ P$5$ W$1$ W$2$ W$33545404240304030$