4) A plant manager employed by a national producer of kitchen products is planning workforce levels for the next three months. An aggregate unit of production requires an average of four labor hours. Forecast demands for the three-month horizon are as follows. Month July August September Workdays 23 16 20 Forecasted Demand (in aggregate units) 2,400 3,000 800 Assume that a normal workday is eight hours. Hiring costs are $500 per worker and layoff costs are $1,000 per worker. Holding costs are $40.00 per aggregate unit held per month. Shortages are not permitted. Assume that the ending inventory was 600 and the manager wishes to have at least 800 units on hand at the end of September. The June work force level is 30 workers. To find the optimal aggregate production plan the following LP is used: Minimize (500H, +1,000F, +4021) M s.to: W₁-W-H,+F=0 W₁-W-H₂+F₁ =0 W₁-W₁-H, +F,=0 P-1+1=2400 P-1+1=3000 P-1, +1,=800 P-46W-0 P-32W=0 P-40W,=0 W₁ =30 1=600 I, ≥800 All variables ≥0