$2023-2024(\frac{16}{1}\frac{?}{2024})$

$1$

A company has two production plants, $P_1$ and $P_2,$ and has to satisfy the demand of three customers, $C_1,C_2$ and $C_3,$ for the next three months. The demands of the customers $C_1,C_2$ and $C_3$ respectively are $500,700$ and $600$ items in Month $1,500,400$ and $600$ items in Month $2$ and $600,500$ and $400$ items in Month $3.$ The demand of the customers in a given Month $i=1,2,3$ can be satisfied by products produced in Months $j$i for $j=1,$dots,$i.$ Hence, the demand of Month $1$ can be satisfied by items produced in Month $1$ only, and the demand of Months $2$ and $3.$ can be satisfied by items produced in Months $1$ and $2_1$ and Months $1,2$ and $3,$ respectively. The items produced in a Month i that are produced to satisfy the demand of the customers in the succeeding Months $j>$i must be stored in a warehouse with a holding cost of $5$ Euros$/$Month for each stored item. The production capacities of the plants $P_1$ and $P_2$ in each Month are $1200$ and $900,$ respectively. In Table $1,$ the unit production costs $($Euro$/$ton$)$ for each plant and month are given.

Table $1$: Unit production costs in Months $1,2$ and $3($Euro$/$ton$).$

$\backslash$table$[[$Plant$,\backslash$table$[[$Production oost$],[$Monsh $1($Euro$/$ton$)]],\backslash$table$[[$Production cost$],[$Month $2($Euro$/$ton$)]],\backslash$table$[[$Production cost$],[$Month $3($Euro$/$ton$)]]],[P_1,20,15,15],[P_2,15,20,25]]$

In Table $2,$ the transportation costs from the plants to the customers, from the plants to the warehouse and from the warehouse, denoted as $W,$ to the customers are reported. Observe that, these costs do not vary over time.

Table $2$: Transportation costs $($Euro$/$ton$).$

$\backslash$table$[[,W,C_1,C_2,C_3$