QUESTION 3 [27 MARKS] PS Distributors sends supplies from two regional warehouses (W1 and W2) to its seven stores and uses a third-party service provider (3PL). As a result of the fuel price increase the 3PL has forwarded then a new distribution rate schedule for the following month (month 6) TRANSPORTATION RATE TO STORES (Rand/ton) WAREHOUSE S1 S2 S3 S5 S6 S7 W1 2 3 11 13 W2 4 9 10 7 S4 8 11 6 7 5 14 PS needs to know the volumes to be transported from each warehouse to the different stores to minimize transportation cost The warehouses have the following capacity constraints WAREHOUSE W1 W2 CAPACITY (tons/month) 500 1 000 PS is uncertain of the demand requirements at the stores for the following month (month 6). However, they have the following demand history for the past 5 months of the stores available MONTHLY DEMAND (tons) MONTH S1 S2 S3 S4 S5 S7 56 223 306 174 229 48 55 220 312 172 227 S6 1 45 111 2 108 4 ann or 4 W2 5 9 7 10 7 14 PS needs to know the volumes to be transported from each warehouse to the different stores to minimize transportation cost. The warehouses have the following capacity constraints: WAREHOUSE CAPACITY (tons/month) 500 1 000 W1 W2 PS is uncertain of the demand requirements at the stores for the following month (month 6). However, they have the following demand history for the past 5 months of the stores available: MONTHLY DEMAND (tons) MONTH S1 S2 S3 S4 S5 S6 S7 1 45 56 111 223 306 174 229 2 55 108 220 312 172 227 3 51 58 105 219 310 175 229 4 50 62 110 220 309 170 230 5 49 60 115 221 311 165 231 48 Use this information to formulate a linear programming model that would enable PS to minimize transport cost (Do not solve the problem) Hint Use a three-month moving average to forecast demand in month 6