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 35 S+95 A+85 H 0.6 S+2A+0.4 H60 0.85 S+2 A+ 3 H60 S+A+H60 2.45 S+5A+4.4 H145 S, A, H0 (Hours cutting 60) (Hours assembly 60) (Hours finishing s60) (Total hours/months 145) (Nonnegativity) The optimal integer solution is to produce solution gives the sling chair(s), Adirondack chair(s), and hammock(s). This profit, which is $ (Type whole numbers.)