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.

TimeNumber of Employees Needed

11:00 a.m.-Noon 9 Employees

Noon-1:00 p.m. 9 Employees

1:00 p.m.-2:00 p.m. 9 Employees

2:00 p.m.-3:00 p.m. 3 Employees

3:00 p.m.-4:00 p.m. 3 Employees

4:00 p.m.-5:00 p.m. 3 Employees

5:00 p.m.-6:00 p.m. 6 Employees

6:00 p.m.-7:00 p.m. 12 Employees

7:00 p.m.-8:00 p.m. 12 Employees

8:00 p.m.-9:00 p.m. 7 Employees

9:00 p.m.-10:00 p.m. 7 Employees

Need help with the below questions.

Thanks

(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 x, be the same variables from part a. Let y = 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 11:00a.m. X: + y28 Noon *. -X2 + y + y28 1:00p.m. *. + x2 + x3 + 1 + y2 + ys 27 2:00p.m. *. + x2 + x3 + x4 +y's + y42 3:00 p.m.*2 + x3 + x4 4 + Y3 21 4:00 pm 3 +24+ 7s + y 2 2 5:00 pm. *4+*g+xo *7 + Y3 + 10 +9724 6:00 p.m. *-* + y + yg > 10 7:00p.m. ***+xy + y + y + y, 210 8:00p.m. 1, +13 + + y;20 9:00 pm. *sy, 7 X *1*2*, *4*3*, Xy, Xy: Y Y Y Y Y Yo Vy. Ygry, 20 Find the optimal solution. Xxx Vs. You Vs. Yusu Y)= (*3 = 6.9: = 5, V3 = 1, Y5 = 1,37 = 4, ) How many part-time shifts are needed, and what is the cost savings compared to the previous schedule? part-time shifts needed 20 cost savings $ 501.60