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

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:
$$\begin{array} { r r r } \text { Product } & \text { Profit per unit } & \text { Setup cost per batch } \\\hline 1 & 9 & 500 \\2 & 10 & 600 \\3 & 12 & 650\end{array}$$
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 X₁,X₂,X₃)= 270,0,0),what values should appear in the shaded cells in the following Excel spreadsheet?
X_i = amount of product i produced
Y_i = 1 if product i produced,0 otherwise
MAX: ^{9 X}₁ ^{+ 10 X}₂ ^{+ 12 X}₃ ^{? 500 Y}₁ ^{? 600 Y}₂ ^{? 650 Y}₃
Subject to: ^{1 X}₁ ^{+ 2 X}₂ ^{+ 2 X}₃ ^{? 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 Y_i = 0,1
X_i ? 0 and integer