Could someone help me see why I'm getting the ones wrong on part c. I need the min., 7pm,8pm, and 9pm answers.
For min I put 30.4x_1+30.4x_2+30.4x_3+30.4x_4+30.4x_5+30.4x_6+30.4x_7+30.4x_8\ +20.8y_1+20.8y_2+20.8y_3+20.8y_4+20.8y_5+20.8y_6+20.8y_7+20.8y_8 but it says wrong
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. Number of Time Employees Needed 11:00 a.m.-Noon Noon-1:00 p.m. 9 1:00 p.m.-2:00 p.m. LD 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. 5:00 p.m.-6:00 p.m. 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. (3) Develop a minimum-cost schedule for part-time employees. (Let x, = the number of part-time employees who start work beginning at hour / where / = 1 = 11:00 a.m., / = 2 = Noon, etc).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, = the number of part-time employees who start work beginning at hour / where / = 1 = 11:00 a.m., / = 2 = Noon, etc). Min 30.4x, + 30.4x2 + 30.4xg + 30.4x4 + 30.4x5 + 30.4vg + 30.4x, + 30.4x s.t. 11:00 a.m. *, 28 Noon 1 +X228 1:00 p.m. *j +X2+x327 2:00 p.m. Kj+xy+*3 + * 421 3:00 p.m. 4:00 p.m. *g +X 4+*5+ *621 5:00 p.m. *4+*5+X6+ X725 6:00 p.m. *5 +*6+*7+x8 2 10 7:00 p.m. X6+X7+X8 2 10 8:00 p.m. X7+*$26 9:00 p.m. Find the optimal solution. (XXXg Xar Kyrks' Xyl x; ) = ( 8, 0, 0, 0, 2, 0, 4, 6 " ) (b) What is the total payroll (in $) for the part-time employees? $ 608 How many part-time shifts are needed? 20 shifts Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts. It is 7 surplus employees schedules from 2-3pm and 4 from 8-0pm. This(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 / where i = 1 = 11:00 a.m., / = 2 = Noon, etc). Min 5 + 30.4xg + 30.4x7 + 30.4xg + 20.8y, + 20.8y2 + 20.8yg + 20.By4 + 20.8ys + 20.8y6 + 20.8v7 + 20.8ys s.t. 11:00 a.m. *1+128 Noon *1 +*2 + V1+V2 28 1:00 p.m. X1 + X2 + X3 + >1+12+1327 2:00 p.m. X1 + X2+ X3 +X4 +12+>3+14 21 3:00 p.m. X2 + *g + X4+ *5 + X3 +14 + >; =2 4:00 p.m. X3 + X4+*5+X6 + 14+ X5 +1621 5:00 p.m. 6:00 p.m. X5 +X6 + X7+X8 + 16 + V7+ys =10 7:00 p.m. X6+X7+X8 + V7 +Vg = 10 x 8:00 p.m. X7+X +7826 Your answer cannot be understood or graded. More Information X 9:00 p.m. X 26 Find the optimal solution. (XXXy' Xar Xy Xyl Xy Xy' Vi Yz' Ya Ya' Va' ye Vy gryg) = ( 0, 0, 0, 0, 0, 0, 0, 6, 8, 0, 1, 0, 1, 0, 4, 0, 0 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 $ 106.40
