Supply Chain Logistics $(3$ points$)$

Consider the following distribution system:

Single product.

Two plants, referred to as plant p$1$ and plant p$2.$

Plant p$2$ has an annual capacity of $40,000$ units.

The two plants have the same production costs.

Two existing warehouses, referred to as warehouse $w1$ and warehouse $w2,$ have identical warehouse handling costs.

Three markets areas, c$1,$ c$2,$ and c$3,$ with demands of $50,000,100,000$ and $50,000,$ respectively, Table $1$ provides distribution cost per unit. For instance, distributing one unit from plant p$1$ to warehouse w$2$ costs $$5.$

Table $1$: DISTRIBUTION COSTS PER UNIT

$\backslash$table$[[\backslash$table$[[$Facility$],[$warehouse$]],$p$1,$p$2,$c$1,$c$2,$c$3],[$w$1,0,3,4,4,5],[$W$2,4,2,3,1,2]]$

Our objective is to find a distribution strategy that specifies the flow of products from the suppliers through the warehouses to the market areas without violating the plant p$2$ production capacity constraints, that satisfies market area demands, and that minimizes total distribution costs. Observe that this problem is significantly easier to solve than the logistics network configuration problem discussed earlier. Here we assume that facility location is not an issue, and we merely attempt to find an effective distribution strategy. For this purpose, consider the following question:

Q# $1)$Show the path $($without this, no credit will be given$)$ for the below question$/$answer$.$

If you only consider C$2,$ and ignore C$1$ and C$3$ completely, what would be the total distribution cost for C$2?$ You need to show the procedure and no credit will be given.

$\backslash$table$[[\backslash$table$[[$Facility$],[$warehouse$]],$p$1,$p$2,$c$1,$c$2,$c$3],[$w$1,4,2,3,3,4],[$W$2,3,3,2,5,1]]$

Q# $2)$Convert the following diagram into the table. $($this question is not related to the above question.

Completely independent. No need for any calculation.