A linear programming computer package is needed. Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 a.m. to 10:00 p.m. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average wage rate for the part-time employees is $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown. Time Number of Employees Needed 11:00 a.m.–Noon 9 Noon–1:00 p.m. 9 1:00 p.m.–2:00 p.m. 9 2:00 p.m.–3:00 p.m. 3 3:00 p.m.–4:00 p.m. 3 4:00 p.m.–5:00 p.m. 3 5:00 p.m.–6:00 p.m. 6 6:00 p.m.–7:00 p.m. 12 7:00 p.m.–8:00 p.m. 12 8:00 p.m.–9:00 p.m. 7 9:00 p.m.–10:00 p.m. 7 One full-time employee comes on duty at 11:00 a.m., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 p.m. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern. (a) Develop a minimum-cost schedule for part-time employees. (Let xi = the number of part-time employees who start work beginning at hour i where i = 1 = 11:00 a.m., i = 2 = Noon, etc). Min s.t.11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. x1, x2, x3, x4, x5, x6, x7, x8 ≥ 0 Find the optimal solution. (x1, x2, x3, x4, x5, x6, x7, x8) = (b) What is the total payroll (in $) for the part-time employees? $ How many part-time shifts are needed? shifts Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts. This answer has not been graded yet. (c) Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. (Let xi be the same variables from part a. Let yi = the number of part-time employees who start work beginning at hour i where i = 1 = 11:00 a.m., i = 2 = Noon, etc). Min s.t.11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. x1, x2, x3, x4, x5, x6, x7, x8, y1, y2, y3, y4, y5, y6, y7, y8, y9 ≥ 0 Find the optimal solution. (x1, x2, x3, x4, x5, x6, x7, x8, y1, y2, y3, y4, y5, y6, y7, y8, y9) = How many part-time shifts are needed, and what is the cost savings (in $) compared to the previous schedule? part-time shifts neededcost savings$

A linear programming computer package is needed. Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 a.m. to 10:00 p.m. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average wage rate for the part-time employees is $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown. Time Number of Employees Needed 11:00 a.m.–Noon 9 Noon–1:00 p.m. 9 1:00 p.m.–2:00 p.m. 9 2:00 p.m.–3:00 p.m. 3 3:00 p.m.–4:00 p.m. 3 4:00 p.m.–5:00 p.m. 3 5:00 p.m.–6:00 p.m. 6 6:00 p.m.–7:00 p.m. 12 7:00 p.m.–8:00 p.m. 12 8:00 p.m.–9:00 p.m. 7 9:00 p.m.–10:00 p.m. 7 One full-time employee comes on duty at 11:00 a.m., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 p.m. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern. (a) Develop a minimum-cost schedule for part-time employees. (Let xi = the number of part-time employees who start work beginning at hour i where i = 1 = 11:00 a.m., i = 2 = Noon, etc). Min s.t.11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. x1, x2, x3, x4, x5, x6, x7, x8 ≥ 0 Find the optimal solution. (x1, x2, x3, x4, x5, x6, x7, x8) = (b) What is the total payroll (in $) for the part-time employees? $ How many part-time shifts are needed? shifts Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts. This answer has not been graded yet. (c) Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. (Let xi be the same variables from part a. Let yi = the number of part-time employees who start work beginning at hour i where i = 1 = 11:00 a.m., i = 2 = Noon, etc). Min s.t.11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. x1, x2, x3, x4, x5, x6, x7, x8, y1, y2, y3, y4, y5, y6, y7, y8, y9 ≥ 0 Find the optimal solution. (x1, x2, x3, x4, x5, x6, x7, x8, y1, y2, y3, y4, y5, y6, y7, y8, y9) = How many part-time shifts are needed, and what is the cost savings (in $) compared to the previous schedule? part-time shifts neededcost savings$

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 37CR

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Related questions

Question

A linear programming computer package is needed.

Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 a.m. to 10:00 p.m. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average wage rate for the part-time employees is $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown.

Time	Number of Employees Needed
11:00 a.m.–Noon	9
Noon–1:00 p.m.	9
1:00 p.m.–2:00 p.m.	9
2:00 p.m.–3:00 p.m.	3
3:00 p.m.–4:00 p.m.	3
4:00 p.m.–5:00 p.m.	3
5:00 p.m.–6:00 p.m.	6
6:00 p.m.–7:00 p.m.	12
7:00 p.m.–8:00 p.m.	12
8:00 p.m.–9:00 p.m.	7
9:00 p.m.–10:00 p.m.	7

One full-time employee comes on duty at 11:00 a.m., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 p.m. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern.

(a)

Develop a minimum-cost schedule for part-time employees. (Let

x_i

= the number of part-time employees who start work beginning at hour i where

i = 1 = 11:00 a.m.,

i = 2 = Noon,

etc).

Min

s.t.11:00 a.m.

Noon

1:00 p.m.

2:00 p.m.