$2.$ ABC Shipping Co$.$ has three factories $-$ F$1,$ F$2,$ and F$3$ with production capacity $30,50,$ and $20$ units per week respectively. These units are to be shipped to three warehouses W$1,$ W$2$ and W$3$ with requirement of $40,25$ and $35$ units per week respectively. The transportation costs $($in Rs$.)$ per unit between factories and warehouses are given below.

a$.$ Write the mathematical model formulation for the problem

b$.$ Find how much units should be transported from factories to warehouses.

W$1$ W$2$ W$3$ Supplies

F$1681030$

F$27111150$

F$3451220$

Demand $402535$