JUST NEED HELP WITH C

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 $7.50 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. a 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 return for another 4 full-time employee comes to work at 1:00 p.m. and the same 4-hours-on, 1-hour-off, 4- 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 i where i = 1 = 11:00 a.m., i = 2 = Noon, etc). Min 30.4x4 +30.4x, +30.4x3 +30.4x4 +30.4x7 +30.4x7 +30.4x, +30.4x7 s.t. 11:00 a.m. X1 28 Noon *1+x28 1:00p.m. *1 + x2+xz>7 2:00 p.m. *1 + x2 + x3 + x2 > 1 3:00p.m. *2 +*3 *3 > 2 4:00 p.m. *3+x4+x3 + xo> 1 5:00 p.m. *4 + x3 + xo+xz> 5 7:00p.m. *o + xy + xg > 10 8:00 p.m. *;+x3 > 0 9:00 p.m. *s > 0 *11*21*3. *4*5*6*7, Xg 20 Find the optimal solution. (* 11 *2X3, 44, 45, 46, 47, *g) = ( 8, 0, 0, 0, 2, , 4, 6 (b) What is the total payroll (in $) for the part-time employees? $ 008 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. There's 7 employees at a surplus that are scheduled from 2-3PM and 4 from 3-9PM which is the desirability of rotation of employees off sooner Score: 0.84 out of 0.84 Comment: (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 xbe 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 30.40x7 + 22.80y1 X s.t. 11:00 a.m. 8 X Noon 1:00p.m. 1 X 2:00 pm 3:00 p.m. 1 X 4:00 p.m. 5:00 p.m. 4 X 6:00 p.m. 6 X 7:00 p.m. 8:00 p.m. 9:00 p.m. * 11 * 2 * 3. *4. *5* *62*7, Xg, Y 11 Y 2 Y 3, 74Y 5 Yr Y 7. YgY20 Find the optimal solution. (Xq, Xq, Xar Y3 4 Y Y Y 7. YgY) - How many part-time shifts are needed, and what is the cost savings compared to the previous schedule? part-time shifts needed 6 X cost savings $ 501.60 X