K&L Corp. manufactures two products that are sold as raw materials to different companies. K&Ls management, basing it on their analysis of their inventory and forecasted demand, specified that the combined production for products A and B must total at least $350$ liters with $600$ hrs$.$ of processing time available. Another thing to consider, they must satisfy one of their VIP client's order of $125$ liters of product A$.$ Product A$\text{'}$s processing time per liter is $2$ hrs$.,$ and product B$\text{'}$s processing time per liter is $1$ hr$.$ K&Ls objective is to satisfy these requirements at a minimum total production cost. Production costs for product A is $$3$ per liter and for product B $$2$ per liter.Questions to answer:$1)$ How much is the minimum total production costs given all the resources and constraints in this case? $(5$ pts$.)$