Working Out:
- X = Num. of bottles sold from Vineyard 1
- Y = Num. of bottle sold from Vineyard 2
- A = Num. of bottles demanded by Rest 1
- B = Num. of bottles demanded by Rest 2
- C = Num of bottles demanded by Rest 3
D = Num of bottles demanded by Rest 4
Revenue = 69A + 67B + 70C + 66D
Cost (Exclusing Shipping) = (23X + 25Y)
X <= 3500 Y <= 3100
A <= 1800 B <= 2300 C <= 1250 D <= 1740
I'm really confused with the shipping table. Can someone please explain how to solve this problem.
Variables
Let $x_{ij}$ be the number of bottles sold from vineyard $i\in \{1,2\}$ to restaurant $j\in \{ 1,2,3,4\}$.
Parameters
Let $c_{ij}$ be the transportation cost from vineyard $i$ to restaurant $j$, let $f_i$ be the production cost for one bottle in vineyard $i$, let $p_j$ be the price of a bottle in restaurant $j$, and finally let $C_i$ and $d_j$ be the capacities and demands in vineyard $i$ and restaurant $j$, respectively.
Objective function
You want to maximize profits, that is $$ \mbox{Maximize } Z= \sum_{i=1}^2\sum_{j=1}^4 (p_j-c_{ij}-f_i)x_{ij} $$ Constraints
Subject to capacity and demand constraints: $$ \sum_{j=1}^4x_{ij} \le C_i \quad \forall i =1,2\\ \sum_{i=1}^2x_{ij} \le d_j \quad \forall j =1,2,3,4\\ x_{ij}\ge 0\quad \forall i =1,2,\;\forall j =1,2,3,4 $$