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The Vandelay furniture company makes bookshelves and tables. Consider the following Linear Programming Model: 4 X₁ = the number of bookshelves made in a day. X2 = the number of tables made in a day. Maximize: Z 50X₁ +50X₂ = Profit ($) Subject to: 20X1 + 12.0X2 <= 100 Labor (hours) 7.8X1 + 10X2 <= 50 Lumber (board-feet) What's the lowest that the profit on a bookshelf can be, without changing the optimal solution? Another way to ask this is, what's the lower bound on the sensitivity range for C₁? (Round your answer to 1 decimal place.)

The Vandelay furniture company makes bookshelves and tables. Consider the following Linear Programming Model: 4 X₁ = the number of bookshelves made in a day. X2 = the number of tables made in a day. Maximize: Z 50X₁ +50X₂ = Profit ($) Subject to: 20X1 + 12.0X2 <= 100 Labor (hours) 7.8X1 + 10X2 <= 50 Lumber (board-feet) What's the lowest that the profit on a bookshelf can be, without changing the optimal solution? Another way to ask this is, what's the lower bound on the sensitivity range for C₁? (Round your answer to 1 decimal place.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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linear programming
The Vandelay furniture company makes bookshelves and tables. Consider the following Linear Programming Model: 4 X₁ = the number of bookshelves made in a day. X2 = the number of tables made in a day. Maximize: Z 50X₁ +50X₂ = Profit ($) Subject to: 20X1 + 12.0X2 <= 100 Labor (hours) 7.8X1 + 10X2 <= 50 Lumber (board-feet) What's the lowest that the profit on a bookshelf can be, without changing the optimal solution? Another way to ask this is, what's the lower bound on the sensitivity range for C₁? (Round your answer to 1 decimal place.)
Transcribed Image Text:The Vandelay furniture company makes bookshelves and tables. Consider the following Linear Programming Model: 4 X₁ = the number of bookshelves made in a day. X2 = the number of tables made in a day. Maximize: Z 50X₁ +50X₂ = Profit ($) Subject to: 20X1 + 12.0X2 <= 100 Labor (hours) 7.8X1 + 10X2 <= 50 Lumber (board-feet) What's the lowest that the profit on a bookshelf can be, without changing the optimal solution? Another way to ask this is, what's the lower bound on the sensitivity range for C₁? (Round your answer to 1 decimal place.)
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