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A Company Produces Three Products Which Must Be Painted,assembled,and Inspected

Question 68

Essay

A company produces three products which must be painted,assembled,and inspected.The machinery must be cleaned and adjusted before each batch is produced.They want to maximize their profits for the amount of operating time they have.The unit profit and setup cost per batch are:
 Product  Profit per unit  Setup cost per batch 19500210600312650\begin{array} { r r r } \text { Product } & \text { Profit per unit } & \text { Setup cost per batch } \\\hline 1 & 9 & 500 \\2 & 10 & 600 \\3 & 12 & 650\end{array}
The operation time per unit and total operating hours available are:
 Operating Time per Unit  Operation  Product 1  Product 2  Product 3  Operating Hours Available  Paint 122400 Assemble 232600 Inspection 243540\begin{array}{c}\text { Operating Time per Unit }\\\begin{array} { l c c c c } \text { Operation } & \text { Product 1 } & \text { Product 2 } & \text { Product 3 } & \text { Operating Hours Available } \\\hline \text { Paint } & 1 & 2 & 2 & 400 \\\text { Assemble } & 2 & 3 & 2 & 600 \\\text { Inspection } & 2 & 4 & 3 & 540\end{array}\end{array}
Based on this ILP formulation of the problem and the optimal solution X1,X2,X3)= 270,0,0),what values should appear in the shaded cells in the following Excel spreadsheet?
Xi = amount of product i produced
Yi = 1 if product i produced,0 otherwise
MAX: 9 X1 + 10 X2 + 12 X3 ? 500 Y1 ? 600 Y2 ? 650 Y3
Subject to: 1 X1 + 2 X2 + 2 X3 ? 400
2 X1 + 3 X2 + 2 X3 ? 600
2 X1 + 4 X2 + 3 X3 ? 540 X1 ? M1 Y1 OR 270 Y1 X2 ? M2 Y2 OR 135 Y2 X3 ? M3 Y3 OR 180 Y3 Yi = 0,1
Xi ? 0 and integer
 A company produces three products which must be painted,assembled,and inspected.The machinery must be cleaned and adjusted before each batch is produced.They want to maximize their profits for the amount of operating time they have.The unit profit and setup cost per batch are:   \begin{array} { r r r }  \text { Product } & \text { Profit per unit } & \text { Setup cost per batch } \\ \hline 1 & 9 & 500 \\ 2 & 10 & 600 \\ 3 & 12 & 650 \end{array}   The operation time per unit and total operating hours available are:   \begin{array}{c} \text { Operating Time per Unit }\\ \begin{array} { l c c c c }  \text { Operation } & \text { Product 1 } & \text { Product 2 } & \text { Product 3 } & \text { Operating Hours Available } \\ \hline \text { Paint } & 1 & 2 & 2 & 400 \\ \text { Assemble } & 2 & 3 & 2 & 600 \\ \text { Inspection } & 2 & 4 & 3 & 540 \end{array} \end{array}   Based on this ILP formulation of the problem and the optimal solution X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>)= 270,0,0),what values should appear in the shaded cells in the following Excel spreadsheet? X<sub>i </sub>= amount of product i produced Y<sub>i </sub>= 1 if product i produced,0 otherwise MAX: <sup>9 X</sup><sub>1 </sub><sup>+ 10 X</sup><sub>2 </sub><sup>+ 12 X</sup><sub>3 </sub><sup>? 500 Y</sup><sub>1 </sub><sup>? 600 Y</sup><sub>2 </sub><sup>? 650 Y</sup><sub>3</sub> Subject to: <sup>1 X</sup><sub>1 </sub><sup>+ 2 X</sup><sub>2 </sub><sup>+ 2 X</sup><sub>3 </sub><sup>? 400</sup> 2 X<sub>1 </sub>+ 3 X<sub>2 </sub>+ 2 X<sub>3 </sub>? 600 2 X<sub>1 </sub>+ 4 X<sub>2 </sub>+ 3 X<sub>3 </sub>? 540 X<sub>1 </sub>? M<sub>1 </sub>Y<sub>1 </sub>OR 270 Y<sub>1 </sub>X<sub>2 </sub>? M<sub>2 </sub>Y<sub>2 </sub>OR 135 Y<sub>2 </sub>X<sub>3 </sub>? M<sub>3 </sub>Y<sub>3 </sub>OR 180 Y<sub>3 </sub>Y<sub>i </sub>= 0,1 X<sub>i </sub>? 0 and integer

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