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Of the following options for the objective function, which is correct for this LP? O O min z = 24 Σ²=1 Σ¼=1 Xij * Xi+1,j+1 + 36 Σi=1 Σj=1 Xij * Xi+2,j+2 2= = 24(X12 + X14 + X23 + X34 +X13 + X24) min Z= 216(x12 + x14 + X23 + X34) + 144(x13 + X24) 2 = 144(x12 + x14 + X23 +X34) + 216(x13 + X24) 216(x12 +14+x23 + x34) +144(x13 + x24) max z = 12²₁₁ Σj=1 Xij * Xi+1,j+1 + 18 Σi=1 Σj=1 Xij * Xi+2,j+2 =1 max min max z =

Of the following options for the objective function, which is correct for this LP? O O min z = 24 Σ²=1 Σ¼=1 Xij * Xi+1,j+1 + 36 Σi=1 Σj=1 Xij * Xi+2,j+2 2= = 24(X12 + X14 + X23 + X34 +X13 + X24) min Z= 216(x12 + x14 + X23 + X34) + 144(x13 + X24) 2 = 144(x12 + x14 + X23 +X34) + 216(x13 + X24) 216(x12 +14+x23 + x34) +144(x13 + x24) max z = 12²₁₁ Σj=1 Xij * Xi+1,j+1 + 18 Σi=1 Σj=1 Xij * Xi+2,j+2 =1 max min max z =

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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Every day, secret, over-worked employees at Wayne Enterprises work two 6-hour shifts producing Batmobiles. These shifts are selected from 12 am - 6 am, 6 am - 12 pm, 12 pm - 6 pm, and 6 pm - 12 am. The following table depicts the number of employees needed during each shift: Shift Time Period 1 2 3 4 12 am - 6 am 6 am - 12 pm 12 pm - 6 pm 6 pm - 12 am Number of Employees Required 13 21 17 11 Bruce Wayne pays all employees working two consecutive shifts, $12 per hour (Note: employees scheduled to work 12 am - 6 am and 6 pm - 12 am would be considered consecutive). Employees whose shifts are not consecutive are paid $18 per hour for the inconvenience. Formulate an LP that can be used to minimize the cost of meeting the daily workforce demands for Batmobile production. To formulate the model, use the following decision variables: Xij = workers working shifts i and j where i, j = {1, 2, 3, 4}
Transcribed Image Text:Every day, secret, over-worked employees at Wayne Enterprises work two 6-hour shifts producing Batmobiles. These shifts are selected from 12 am - 6 am, 6 am - 12 pm, 12 pm - 6 pm, and 6 pm - 12 am. The following table depicts the number of employees needed during each shift: Shift Time Period 1 2 3 4 12 am - 6 am 6 am - 12 pm 12 pm - 6 pm 6 pm - 12 am Number of Employees Required 13 21 17 11 Bruce Wayne pays all employees working two consecutive shifts, $12 per hour (Note: employees scheduled to work 12 am - 6 am and 6 pm - 12 am would be considered consecutive). Employees whose shifts are not consecutive are paid $18 per hour for the inconvenience. Formulate an LP that can be used to minimize the cost of meeting the daily workforce demands for Batmobile production. To formulate the model, use the following decision variables: Xij = workers working shifts i and j where i, j = {1, 2, 3, 4}
Of the following options for the objective function, which is correct for this LP? O min 2 = min max 2 = 24(x12 + X14 + X23 + X34 + X13 + X24) min z = 216(x12 + x14 + X23 + X34) + 144(X13 + X24) * = 144(x12 + x14 + X23 + X34) +216(x13 + X24) 216(x12 + X14 + X23 + X34) + 144(x13 + X24) 12 Σ max max z = 24Σ 1Σ=1&ij*Wi+1+1+ 36 ΣΣ=1&ij*Wi+23+2 •j=1 * Ξ 4 i=1 Σ =1 Wij * Wi+1,j+1 + 18 Σ 1 Σ=1ij * Xi+2,j+2 i=1
Transcribed Image Text:Of the following options for the objective function, which is correct for this LP? O min 2 = min max 2 = 24(x12 + X14 + X23 + X34 + X13 + X24) min z = 216(x12 + x14 + X23 + X34) + 144(X13 + X24) * = 144(x12 + x14 + X23 + X34) +216(x13 + X24) 216(x12 + X14 + X23 + X34) + 144(x13 + X24) 12 Σ max max z = 24Σ 1Σ=1&ij*Wi+1+1+ 36 ΣΣ=1&ij*Wi+23+2 •j=1 * Ξ 4 i=1 Σ =1 Wij * Wi+1,j+1 + 18 Σ 1 Σ=1ij * Xi+2,j+2 i=1
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Please identify all of the correct constraints for the model. ΟΣ=1&i U Π U Π Π Π = Π (13 + 21 + 17 + 11) Vj 214 Χ 224 Χ 234 X13 + x23 +34 ≤ 17 11 X14X24 + X34 ≥ 11 212 Χ 213 Χ 214 = 13 X14X24X34 ≤ 11 €12 Χ 223 Χ 224 = 21 x12 +13 + 14 ≥ 13 X12 + x23 + x24 ≤ 21 213 Χ 223 Χ 34 17 x13x23x34 ≥ 17 ΟΣ=1&ij < (13 + 21 + 17 + 11) Va X12 + x23 + x24 ≥ 21 ΟΣ=1 €i; > (13 + 21 + 17 + 11) Vj x12 + x13 + 14 ≤ 13
Transcribed Image Text:Please identify all of the correct constraints for the model. ΟΣ=1&i U Π U Π Π Π = Π (13 + 21 + 17 + 11) Vj 214 Χ 224 Χ 234 X13 + x23 +34 ≤ 17 11 X14X24 + X34 ≥ 11 212 Χ 213 Χ 214 = 13 X14X24X34 ≤ 11 €12 Χ 223 Χ 224 = 21 x12 +13 + 14 ≥ 13 X12 + x23 + x24 ≤ 21 213 Χ 223 Χ 34 17 x13x23x34 ≥ 17 ΟΣ=1&ij < (13 + 21 + 17 + 11) Va X12 + x23 + x24 ≥ 21 ΟΣ=1 €i; > (13 + 21 + 17 + 11) Vj x12 + x13 + 14 ≤ 13
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Which statement represents the correct sign restriction for our decision variable? It is not necessary to include a sign restriction. X12, 14, X23, X34 0 X13, X240 Xij ≤0 Vi, j xįj urs (unrestricted) Vi, j xij≥0 Vi, j
Transcribed Image Text:Which statement represents the correct sign restriction for our decision variable? It is not necessary to include a sign restriction. X12, 14, X23, X34 0 X13, X240 Xij ≤0 Vi, j xįj urs (unrestricted) Vi, j xij≥0 Vi, j
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