### Problem I $(40\%)$Pratama is a company that produces precast concrete piles, with factories located in cities A$,$ B$,$ and C$.$ Its distribution centers are located in cities P and Q$.$ The capacities of the three factories are respectively $(3+$N$3)*100,150,$ and $120.$ The demand at the two distribution centers is $270$ and $(2+$N$3)*100.$ The transportation cost per concrete pile per kilometer is Rp$.(3+$N$3).$ The distance between factories and distribution centers is $($in km$)$:$||$ P $|$ Q $||---|---|---||$ A $|100$ km $|200$ km $||$ B $|300$ km $|300$ km $||$ C $|200$ km $|100$ km $|$Find the optimal solution for the minimal transportation cost from the factories to the distribution centers.### Problem II $(20\%)$Formulate the mathematical model for Problem I.### Problem III $(40\%)**$Specialist Workers Table$**|$ Work $|$ Worker $1|$ Worker $2|$ Worker $3|$ Worker $4|$ Worker $5||------|----------|----------|----------|----------|----------||1|5+$N$3|9|2+$N$1|8|6||2|4|7|8|4|5||3|10+$N$1|7+$N$3|\_|9+$N$3|3||4|5|4+$N$3|\_|9|7||5|10+$N$2|7|5|4|3|$Note: The numbers in the table represent the time required to complete each job by each specialist worker. Job $4$ cannot be done by Specialist Worker $3.$Find the optimal solution $($shortest total time$)$ for completing all the jobs.

N$1=0$

N$2=3$

N$3=8$