Case "4" Monitoring the productivity of the production line to meet market requirement, the productivity of line change monthly between maximum and minimum productivity according to the curve shown in figure "2" 61 5 4 M 3 2 1 -211 -TT TT 2 TT 510 NIE FIN 3TT 2 2 Figure "2" : Relation of productivity per month Also the quality department calculate the profit of the factory monthly to make sure that the productivity meet market requirement The equation of the profit is given by: Profit (day) = 4day - day2 + 3. Eq. 4.1 Referring to case "4" a) For quality control purposes, the factory should know the quantity of consumption during the month as shown in figure 2; write the equation for the quantity of consumption during the month to know the quantity per day. b) For equation 4.1, use second order derivative to analyse the following: 0 Maximum and minimum value of the factory profit. 0 The interval of increasing and decreasing of profit