Consider the forecasted demand pattem in the table given below. Assume that you have 30 production hours of inventory at the beginning of period 0. The same 30 production hours are to be made available at the end of the six-month planning horizon. The manufacturing facility can support a maximum regular production rate of 90 production hours/month. Cumulative forecasts (in production hours) Month Forecast demand Cumulative demand 1. September 30 2. October 30 60 3. November 120 180 4. December 270 5. January 330 6. February 30 360 90 60 Cost structure and initial conditions Cost of regular time labor 200 TL production hour Cost of overtime 300 TL /production hour Cost of hiring 120 TL /production hour Cost of laying off 70 TL / production hour Cost of carrying inventory 40 TL / production hour Initial inventory 30 production hours Initial workforce 25 production hours / month a. Offer a pure chase production strategy and calculate total cost over the planning horizon. Workforce Workforce laying Regular time Overtime Inventory Total cost hiring cost off cost cost cost cost b. Offer a pure level production strategy and calculate total cost over the planning horizon. Workforce Workforce Regular Overtime Inventory Total cost hiring cost laying off cost time cost cost cost NOTE: THE QUESTION IS REQUESTED TO BE RESOLVED IN THE AGGREGATE PLANNING USING LINEAR PROGRAMMING FRAMEWORK USING THE FOLLOWING VARIABLES AND FORMULAS: DECISION VARIABLES t=1,...,n t=1,...,n Wt=workforce size for montht, t=1,...,n Ht=number of employees hired at the beginning of month t, Lt=number of employees laid off at the beginning of month t, Pt=number of units produced in month t, t=1,...n It=inventory at the end of month t, t=1,...,n St=number of units stoked out backlogged at the end of month t, Ct=number of subcontracted for month t, t=1,...,n Ot=number of overtime hours worked in month t, t=1,...,n t=1,..., OBJECTIVE FUNCTION: aw. + bo, + c. + dL. + el. + rst + g. + mc. t t t a= Regular-time labor cost ($ x hour x day) b=Overtime labor cost C= Cost of hiring d= Cost of layoffs e= Cost of inventory f= Cost of stocking out &= Cost of materials m= Cost of subcontracting EQUATIONS: Workforce, hiring, and layoff constraints: W+ = W1-1 + H-L Inventory balance constraints: It-1 +P+ + Ct = Dt + St-1 + 1+ - St