QUESTION 1 1.1. Explain briefly what an x-chart and an R -chart do. 1.2. 1.3. [10] (4) Explain how a person using 2-sigma control charts will more easily find samples "out of limits" than 3-sigma control charts. Define in detail time fences in master scheduling process. QUESTION 2 (4) (2) [15] 2.1. Pex (Pty) Ltd. manufactures wooden boxes with lids. Pex wants to plan ahead in order to address the variations in the seasonal demand for its products. A planning. horizon of 6 months is used. The forecast shown in the table below has been prepared for the wooden boxes and lids products. Period July Forecast 1000 August 1200 1500 September October 1900 November December Total 1800 1600 9000 Manufacturing these products will incur the following costs; Items Regular time Overtime Inventory carrying costs Subcontracting costs Back order Quantity per month 1400 Number of workers 20 Cost (R) per unit 15,00 20,00 10,00 30,00 40,00 The products must be produced at a steady rate of a regular time output. Any fluctuation in the demand must be absorbed using inventory and in other certain cases it is allowable to use backlogs to make-up for any discrepancies. As the steady rate output is required, the use of overtime and subcontracting is prohibited. At the beginning of July, 200 on hand inventory are recorded. Each worker can produce 70 units per month. Apply the trial and error method and present aggregate plan using the information provided and calculating the costs involved in delivering the required units to meet demand. (15)