Alfred Pennyworth Corporation is in the business of manufacturing bearings and grappling hooks. The process of production for each type of accessory for Batmans utility belt requires no small measure of crafting and polishing. Three hours of crafting and two hours of polishing are needed in making one batarang. Meanwhile, two hours of crafting and one hour of polishing are needed in making one grappling hook.

The next production period programs a maximum of 480 hours of crafting time and 280 hours of polishing time. Profits of P2,000 and P1,200 are made for each batarang and grappling hook produced, respectively.

Formulate and solve the linear programming production mix situation to find the optimal combination of batarangs and grappling hooks that yields the highest profit. What is the best graphical approach for the problem and why?