A company manufactures two different sizes of boat lifts. Each size requires some time in the welding and assembly department and sometime in the parts and packaging department. The smaller lift requires ¾ hour in welding and assembly and 1 2/3 hours in parts and packaging. The larger lift requires 1 1/2 hours in welding and assembly and 1 hour in parts and packaging. The factory has 156 hours/day available in welding and assembly and 174 hours/day available in parts and packaging. Furthermore, daily demand for the lifts is at most 90 large and at most 100 small, and profits are $200 for each large lift and $120 for each small lift.

(a) How many of each type of boat lift should be manufactured each day in order to maximize the profit? Find the maximum profit.

(b) At the optimal solution in part (a), analyze the company's constraints (welding and assembly hours, parts and packaging hours, and demand) to determine the "Amount Available," "Amount Used," and "Amount Not Used (Slack)."

(c) Obtaining additional quantities of which constraint items would have the potential to increase the company's profit? Explain.

(d) Obtaining more of which constraint item would not increase profit? Explain.