1. Fresh strawberry supply involves growing, picking, pre-cooling, sorting, packing and then distributing different sized plastic containers (or punnets) of strawberries to different cus- tomers. The pre-cooling, sorting and packing operations of Berrymore P/L all take place in on-farm packing sheds that are within a few hundred metres of the strawberry fields. The company has signed a contract to supply 120 thousand 250g punnets of premium strawber- ries to Coles supermarkets in Adelaide in June. The only Berrymore P/L farms that can supply strawberries at that time of year are the four farms the company owns in Queensland and Western Australia. The maximum numbers of punnets that can be supplied by these farms in June are reported in Table 1. This table also reports the total costs that would be incurred in landing the punnets in Adelaide. Recent supply disruptions caused by sabotage and heavy rainfall have made the company aware of just how easily supplies of premium strawberries can be disrupted by unforeseen environmental, economic and criminal events. Partly to minimise the risks associated with such events, the company has decided that (i) no one farm can supply more than 50 thousand punnets; (ii) there can be no more than two suppliers from WA; and (iii) if the Albany farm is a supplier, then the Beerwah farm cannot be a supplier. (a) (10 marks) Let x; denote the number of punnets supplied by farm i, and let zi be a binary variable that takes the value 1 if xi >0 (and 0 otherwise). Formulate a linear program that will allow Berrymore P/L to land 120 thousand punnets of strawberries in Adelaide at minimum cost. (b) (5 marks) Use the Integer and Mixed Integer Programming (IMIP) module in Excel QM to solve the LP formulated in part (a). Report the total number of punnets to be supplied by each farm and the associated total landing cost. Table 1: Strawberry Suppliers Farm 1. Beerwah 2. Albany 3. Wanneroo 4. Bullsbrook Maximum Supply ('000 punnets) 110 28 61 75 Landing Cost ($ per punnet) 2.60 2.40 2.20 2.25