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 + 90 H 0.5 S+2 A+ 0.6 H ≤ 50 0.85 S+2 A+ 3 H ≤ 50 S+A+H≤ 50 2.35 S +5 A+ 4.6 H≤ 120 S, A, H 20 (Hours cutting ≤ 50) (Hours assembly ≤ 50) (Hours finishing ≤50) (Total hours/month ≤ 120) (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.)

Practical Management Science
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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 + 90 H
0.5 S + 2 A+ 0.6 H ≤ 50
0.85 S + 2 A + 3 H ≤ 50
S + A+H≤ 50
2.35 S + 5 A + 4.6 H≤ 120
S, A, H≥0
The optimal integer solution is to produce
the
profit, which is $
(Type whole numbers.)
(Hours cutting ≤ 50)
(Hours assembly ≤ 50)
(Hours finishing ≤ 50)
(Total hours/month ≤ 120)
(Nonnegativity)
sling chair(s),
Adirondack chair(s), and
hammock(s). This solution gives
Transcribed Image Text: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 + 90 H 0.5 S + 2 A+ 0.6 H ≤ 50 0.85 S + 2 A + 3 H ≤ 50 S + A+H≤ 50 2.35 S + 5 A + 4.6 H≤ 120 S, A, H≥0 The optimal integer solution is to produce the profit, which is $ (Type whole numbers.) (Hours cutting ≤ 50) (Hours assembly ≤ 50) (Hours finishing ≤ 50) (Total hours/month ≤ 120) (Nonnegativity) sling chair(s), Adirondack chair(s), and hammock(s). This solution gives
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