W$1-1.($Raw Material Acquisition$)$ For its weekly operations, XYZ receives raw materials from two sources using large tank truck. Each truckload from Eco Petro Ltd contains $2$ tons of Raw Material A and $2$ tons of Raw Material B at a cost of $$20,000.$ Each truckload from Clean NRG contains $1$ ton of Raw Material A and $3$ tons of Raw Material B at a cost of $$15,000.$ XYZ requires at least $8$ tons of Raw Material A and at least $12$ tons of Raw Material B per week. XYZ is to determine how many truckloads should be purchased per week from each source. State the optimal solution, optimal value, the slack$/$surplus variables, range of optimality of each coefficient, reduced costs, range of optimality of each constraint, and dual prices