RVW buys $15$ used VW$\text{'}$s at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW$\text{'}$s specifications, RVW sells $10$ each to three different used car lots. There are various costs associated with the average purchase and transportation prices form each auction to each repair shop. Also, there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below.

Repair Shops

Used Car lots

S$1$ S$2$

L$1$

L$2$

L$3$

Auction $1$

$550,500$

S$1250,300$

$500$

Auction $2$

$600,450$

S$2$

$350$

$650$

$450$

What is the minimum Cost

$29000$

$17500$

$32000$

$25500$