A gardening supply company manufactures two types of mulch bins – the Compacto and the Enviro. The production of each bin involves a certain amount of moulding, pressing and assembly as indicated below. Department Mulch Bin Compacto Enviro Moulding 5 hours 6 hours Pressing 8 hours 5 hours Assembly 9 hours 14 hours Next month, the company has maximum available capacities of 630 hours for assembly, 300 hours for moulding and 400 hours for pressing. The company has advance orders for 15 Compacto mulch bins and for 10 Enviro mulch bins and is committed to supplying these next month. The same profit of $6,000 is made from the sale of each mulch bin. (i) How many Compacto and Enviro mulch bins should be manufactured next month to fulfill advance orders and maximize profits? How much profit will be made? (Assume that partially completed mulch bins can be manufactured but that only completed bins can be sold for profit. Bins on advance order have not yet been paid for.) (50 marks) (ii) At the optimum production mix for next month, which if any, of the three departments has any excess capacity, i.e. hours available that are not used? Indicate the amount of any excess capacity in hours. (10 marks) (iii) If the profit from the sale of each Enviro mulch bin increases from $6,000 to $15,000 because of its appearance on a popular TV gardening show, how would this affect the proposed production mix for the coming month? (20 marks) QUESTION 2 (45 marks) A steel processing plant supplies lengths of seamless pipe for the oil industry. The pipes are produced to a specified length of 10,000±100 mm. Pipes that are outside the upper or lower tolerance value are considered to be scrap. Samples of four (4) pipes are taken every hour to monitor the state of production. The results of sampling during the most recent 15 hour period are given in the table below. Sample No. Sample average mm Sample Range mm 1 2 3 4 5 10,022 10,014 10,042 10,004 10,028 45 105 30 85 65 6 7 8 9 10 10,006 9,996 9,998 10,046 10,032 25 55 85 100 75 11 12 13 14 15 10,024 10,030 10,016 10,044 9,998 60 35 90 45 75 (i) Calculate the control limits for the range and sample average control charts and plot the control charts for the process. (25 marks) (ii) Determine the relative precision class and calculate modified control limits if this is warranted. Clearly indicate whether or not modified limits are needed. (5 marks) (iii) Comment on the state of production. In particular indicate whether or not the range and sample averages are in control, whether or not any scrap is being produced and whether or not the grand average value is appropriate. (15 marks) QUESTION 3 (75 marks) The Supersports Company supplies boxed pairs of soccer boots to distribution centres in Warwick, Toowoomba and Ipswich from existing warehouses in Brisbane and Sydney. Supersports is considering locating a warehouse at the Gold Coast. Annual capacity in the warehouses is shown in the right-hand column, while annual demand is shown in the bottom row of the Table below. Transportation costs per pair of boots are shown in the small boxes. For example the cost to ship one pair of boots from Brisbane to Warwick is $2.37. Source Destination Capacity Warwick Toowoomba Ipswich Brisbane $2.37 $2.25 $2.89 12,000 12,000 Sydney $2.00 $3.00 10,000 $3.27 10,000 Gold Coast $2.13 6,000 $2.50 12,000 $1.75 18,000 Demand 6,000 22,000 12,000 40,000 What is the optimum transportation plan to minimise delivery costs and what is the minimum total cost to Supersports. Note you must find solutions via iterations and not just putting the results from using spreadsheet or software package.