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}

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}

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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Question

Please identify all of the correct constraints for the model.
ΟΣ 12
=
(13 +21 +17+11) Vj
214 Χ 224 Χ 234 = 11
x13x23x34 ≤ 17
X14X24X34 ≥ 11
212 Χ 213 Χ €14 13
X14X24 + x34 ≤ 11
212 Χ 223 Χ 24 = 21
x12 + x13x14 ≥ 13
x12 + x23 + x24 ≤ 21
213 Χ 223 Χ 234 17
X13 + x23 + x34 ≥ 17
Σ=1 €i; < (13 + 21 + 17 + 11) Vj
x12 + x23 + x24 21
ΟΣ=1&i; > (13 + 21 + 17 + 11) Vj
12 13 14 ≤ 13

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}

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