Question $4(15$ points$)$

Consider a city network with water reservoirs consisting of four cities: Ankara, Bursa, Canakkale, and

Denizli. Ankara and Bursa have water reservoirs out of these four cities. These cities can make water transfer

to other cities when there is a drought in a city.

In the summer, the drought was felt harsh in $$anakkale and Denizli. Canakkale needed $50$ units and

Denizli needed $60$ units of waters from the reservoirs. The reservoir at Ankara has $70$ units of water and

the reservoir at Bursa has $80$ units of water. Cost of the water flow per unit from Ankara to $$anakkale is

$(a**1000)$ TL$,$ from Ankara to Denizli is $(b**1000)$ TL$,$ from Bursa to $$anakkale is $(c**1000)$ TL$,$ and from

Bursa to Denizli is $(d**1000)$ TL$.$ Take $a$ as the $4$th from the last digit of your student number, take $b$ as the

$3$rd from the last digit of your student number, take $c$ as the $2$nd from the last digit of your student number,

and take $d$ as the last digit of your student number. If any of $a,b,c$ or $d$ happens to be $0,$ take that one as

Formulate a linear programming problem to determine the number of units to be sent from each

reservoir to $$anakkale and Denizli, aiming to minimize the total cost.

Convert the problem into its standard form.

Solve the problem analytically.

Use CVXPY to validate your solution. You can check this tutorial for a linear programming example

this link.