Bangs Leisure Chairs produces three types of hand-crafted outdoor chairs:sling chairs, Adirondack chairs, and hammocks. After reviewing the labor required for each new type of chair, the following linear optimization model for profit was found, where is the number of sling chairs produced, Ais 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 4 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 0.6S+2 A+0.6 HS 60 (Hours cutting s60) 0.75 9+2 A3 HS 60 (Hours assembly s 60) TO S.A+HS60 (Hours finishing s60) 2.35 S 5 A+4.6 HS 145 (Total hours/months 145) S, A, H20 (Nonnegativity) on The optimal Integer solution is to produce sing chairs). Adirondack chairs), and hammock(u). This solution gives the profit, which is $ (Type whole numbers.)