Bangs Leisure Chairs produces three types of hand-crafted outdoor chairs: sling chairs, Adirondack chairs, and hammocks. After reviewing the labor required for each type of chair, the following linear optimization model for profit was found, where S is the number of sling chairs produced, A is the number of Adirondack chairs produced, and H is the number of hammocks produced. Implement the linear optimization model and find an optimal solution, ensuring that the number of units produced is integer-valued. How much difference is there between the optimal integer solution objective function and the linear optimization solution objective function? Would rounding the continuous solution have provided the optimal integer solution? Maximize Profit = 40 S + 95 A + 90 H 0.6 S + 2 A + 0.5 H = 40 (Hours cutting $ 40) 0.75 S + 2 A + 3 H $ 40 (Hours assembly s 40) S + A +H$ 40 (Hours finishing = 40) 2.35 S + 5 A + 4.5 H $ 90 (Total hours/month $ 90) S, A, H20 (Nonnegativity) The optimal integer solution is to produce sling chair(s), Adirondack chair(s), and hammock(s). This solution gives the profit, which is $. (Type whole numbers.) maximum minimumA community playhouse needs to determine the lowest-cost production budget for an upcoming show. They have to determine which set pieces to construction and which to rent. The organization has only two weeks to construct the set. The theater has two carpenters who work up to 12 hours a week, each at $12 an hour. Additionally, the theater has a scenic artist who can work 15 hours per week to paint as needed at $16 per hour. The set needs 20 flats (walls), two hanging drops, and three wooden tables (props). The number of hours required for each piece for carpentry and painting is shown below. Flats, hanging drops, and props can also be rented at a cost of $75, $500, and $400 each, respectively. How many of each unit should be built by the theater and how many should be rented to minimize total cost? Click the icon to view the table of carpentry and painting hours. The optimal integer solution is to build flat(s) and rent ]flat(s); build ] hanging drop(s) and rent hanging drop(s); build prop(s) and rent ]prop(s). This solution gives the V cost, which is $ (Type whole numbers.) maximum - X minimum Carpentry and Painting Hours Carpentry Painting Flats 0.5 3.0 Hanging Drops 2.0 12.0 Props 3.0 4.0 Print Done