Indiana's prison budget allows it to consider four new installations next year. They are X₁ = 1 if maximum security prison in Ft. Wayne, = 0 otherwise X₂ = 1 if minimum security prison in Bloomington, = 0 otherwise X3 = 1 if halfway house in Indianapolis, 0 otherwise X4 = 1 if expanded tricounty jail in South Bend, O otherwise The state wants to maximize the number of people that can be "served," while only building one of the two prisons (X₁ or X₂) and observing cost and space limitations. Here is the formulation: maximize number served = 3,000X₁ + 900X₂ + 4,000X3 + 1,500X4 subject to X₁ + X2 4X1 + 2X2 + 7X3 + 3X4 3.5X₁ + 1X₂ +2.5X3 + 9X4 <= 1 prison <= 12 acres available <= 12 million dollars budgeted a. What is the optimal number that can be served?
Indiana's prison budget allows it to consider four new installations next year. They are X₁ = 1 if maximum security prison in Ft. Wayne, = 0 otherwise X₂ = 1 if minimum security prison in Bloomington, = 0 otherwise X3 = 1 if halfway house in Indianapolis, 0 otherwise X4 = 1 if expanded tricounty jail in South Bend, O otherwise The state wants to maximize the number of people that can be "served," while only building one of the two prisons (X₁ or X₂) and observing cost and space limitations. Here is the formulation: maximize number served = 3,000X₁ + 900X₂ + 4,000X3 + 1,500X4 subject to X₁ + X2 4X1 + 2X2 + 7X3 + 3X4 3.5X₁ + 1X₂ +2.5X3 + 9X4 <= 1 prison <= 12 acres available <= 12 million dollars budgeted a. What is the optimal number that can be served?
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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Transcribed Image Text:Indiana's prison budget allows it to consider four new installations next year. They are
x₁ = 1 if maximum security prison in Ft. Wayne,
= 0 otherwise
X₂ = 1 if minimum security prison in Bloomington,
= 0 otherwise
X3 = 1 if halfway house in Indianapolis, 0 otherwise
X4 = 1 if expanded tricounty jail in South Bend, O otherwise
The state wants to maximize the number of people that can be "served," while only building one of the two prisons (X₁ or X₂) and observing cost and space
limitations. Here is the formulation:
maximize number served = 3,000X₁ + 900X₂ + 4,000X3 + 1,500X4
subject to
X₁ + X2
4X1 + 2X2 +7X3 + 3X4
3.5X1 + 1X2 + 2.5X3 + 9X4
<= 1 prison
<= 12 acres available
<= 12 million dollars budgeted
a. What is the optimal number that can be served?
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