h) Optimal solution = (x1, x2) = (0.667, 0.667). P = $12,000. 2.7 a) objective function Z = x1 + 2x2 functional constraints x1 + x2 5 ≤ x1 + 3x2 9 ≤ nonnegativity constraints x1 0, x2 0 ≥ ≥ b & e) c) Yes. d) No. 2.8 a) objective function Z = 3x1 + 2x2 functional constraints 3x1 + x2 9 ≤ x1 + 2x2 8 ≤ nonnegativity constraints x1 0, x2 0 ≥ ≥ b & f) c) Yes. d) Yes. e) No. 2.9 a) As in the Wyndor Glass Co. problem, we want to find the optimal levels of two activities that compete for limited resources. We want to find the optimal mix of the two activities. Let W be the number of wood-framed windows to produce. Let be the number of aluminum-framed windows to produce. A The following table gives the data for the problem: Resource Usage per Unit of Activity Amount of Resource Wood-framed Aluminum-framed Resource Available Glass 6 8 48 Aluminum 0 1 4 Wood 1 0 6 Unit Profit $60 $30 b) The decisions to be made are how many windows of each type to produce. The constraints on the decisions are the amounts of glass, aluminum and wood available. In addition, negative production levels are not possible. The overall measure of performance for the decisions is the profit to be made.
h) Optimal solution = (x1, x2) = (0.667, 0.667). P = $12,000. 2.7 a) objective function Z = x1 + 2x2 functional constraints x1 + x2 ≤ 5 x1 + 3x2 ≤ 9 nonnegativity constraints x1 ≥ 0, x2 ≥ 0 b & e) c) Yes. d) No. 2.8 a) objective function Z = 3x1 + 2x2 functional constraints 3x1 + x2 ≤ 9 x1 + 2x2 ≤ 8 nonnegativity constraints x1 ≥ 0, x2 ≥ 0 b & f) c) Yes. d) Yes. e) No. 2.9 a) As in the Wyndor Glass Co. problem, we want to find the optimal levels of two activities that compete for limited resources. We want to find the optimal mix of the two activities. Let W be the number of wood-framed windows to produce. Let A be the number of aluminum-framed windows to produce. The following table gives the data for the problem: Resource Usage per Unit of Activity Amount of Resource Wood-framed Aluminum-framed Resource Available Glass 6 8 48 Aluminum 0 1 4 Wood 1 0 6 Unit Profit $60 $30 b) The decisions to be made are how many windows of each type to produce. The constraints on the decisions are the amounts of glass, aluminum and wood available. In addition, negative production levels are not possible. The overall measure of performance for the decisions is the profit to be made.
Solution-manual-for-Introduction-to-Management-Science-A-Modeling-and-Case-Studies-5th-edition-Frederick-S-Hillier.docx