Penny Chairs received financing from Funance Inc. to produce three types of outdoor chairs that are ideally suited to the beach, pool, and pa$$os: sling chairs, Adirondack chairs, and hammocks. At its Bruderheim factory, the unit profit for these chairs is $$40,$ $$100,$ and $$90$ respec$$vely$.$ Addi$$onally$,$ each type of chair requires cu$$ng$,$ assembly, and finishing. Workers are available to produce these chairs have $120$ hours available per month however they cannot spend more than $50$ hours per month on any one ac$$vity $($i$.$e$.$ cu$$ng$,$ assembly, and finishing$).$ Sling chairs are made up of ten wood pieces for the frame and one piece of cloth. The cu$$ng of the wood takes $30$ minutes. Assembling includes sewing the cloth and the atachment of rivets, screws, and fabric. This takes $45$ minutes per chair. The finishing step involves sanding, staining, and varnishing chair parts and takes one hour per chair. Adirondack chairs take two hours for the cu$$ng phase as well as the assembly phase whereas the finishing stage takes one hour. For a hammock, cu$$ng takes $0\mathrm{.}4$ hours, assembly takes three hours, and finishing takes one hour.

A$.$ Penny Chairs wants to determine how much of each chair they should produce at their Bruderheim factory to maximize profit B$.$ Penny Chairs has u$$lized AI to reduce all the above $$mes by $10\%$ but the AI program license will cost $$300$ per month. Should they implement the AI program?