Coca Cola $$ecek $($CC$)$ is planning for the production of its soft drinks in Turkey for the next $6$

months. The demand in two regions are given below $($in million liters$)$

Region M$1$ M$2$ M$3$ M$4$ M$5$ M$6$

$9914121213$

Central and

Eastern

$7789910$

There are two plants in Turkey: one in Ankara and another in Istanbul. The plant in Ankara

is primarily responsible for meeting the customer demand in Central and Eastern Turkey,

while the plant in Istanbul is responsible for meeting customer demand in Western Turkey.

The soft drinks are only sold in $1$ lt or $2$ lt bottles. Traditionally, $60\%$ of demand is for $2$ lt

bottles and $40\%$ is for $1$ lt bottles in all markets. The production is done at two steps. The first

step is the bottling stage and it is completely automated. Each plant have a single bottling

system which can bottle either $1$ lt or $2$ lt bottles at a time. If they only process $2$ lt bottles,

Ankara plant can bottle $6,000$ bottles and Istanbul plant can bottle $9,000$ bottles per hour. If they

process only $1$ lt bottles, Ankara plant can bottle $10,000$ bottles and Istanbul plant can bottle

$15,000$ bottles per hour. Bottling systems work for $24$ hours a day and $30$ days a month. There

is no setup time or cost for switching from $1$ lt bottles to $2$ lt bottles or vice versa.

The second step is the packaging and it is completely manual. Current workforce level for

packaging is $60$ employees in Ankara and $100$ employees in Istanbul. Each employee can

package up to $100,000$ liters of soft drink per month. Monthly wages are $1,200$ TL per month.

Hiring cost and cost of lay$-$off are $1,500$ TL and $2,000$ TL per employee, respectively.

The company also has the option to produce in Ankara and ship to Western Turkey, or produce

in Istanbul and ship to Central and Eastern Turkey. Moving soft drinks from Istanbul to Central

and Eastern Turkey or from Ankara to Western Turkey costs an additional $0\mathrm{.}1$ TL per liter.

Inventory is carried only in the packaged form. However inventory cannot be carried for more

than $1$ month due to perishability of the product. Inventory holding costs are $0\mathrm{.}05$ TL per liter

per month for both plants. Initial inventories are $0$ at both plants. Backlogging is not allowed.

CCI aims to minimize its inventory holding, transportation, workforce, hiring and laying$-$off

costs subject to the constraints discussed above. Formulate the problem as a mathematical

program. Define the variables, constraints, and the objective function explicitly and show your

work clearly.