0 Preface Blue Ridge Beverages (BRB) manufactures 3 different products each with a different commercial value per ton given in Table 1. Table 1: Comercial Price of each product (dollars per ton) Root Beer 11 Ginger Beer 24 Cream Soda 43 There are 8 customers (a mixture of wholesalers, chain retailers, and small retailers) each of which has a minimum demand (Table 2) and a maximum capacity (Table 3) for each of the products 12 Table 2: Demand (1000s of tons) of each customer for each product C 1 C 2 C 3 C4 C 5 C 6 C 7 C 8 Root Beer 160 60 54 33 8 1.25 0.46 0.104 Ginger Beer 120 81 31 40 6 2.25 0.36 0.072 Cream Soda 150 44 82 27 7.5 1.5 0.42 0.024 Table 3: Capacity (1000s of tons) of each customer for each product C 1 C2 C 3 C4 C 5 C 6 C 7 C8 Root Beer 170 60 84 37 8.5 1.5 0.6 0.14 Ginger Beer 130 81 65 44 6.5 2.5 0.44 0.12 Cream Soda 160 44 110 31 8 1.75 0.56 0.1 BRB must meet the demand of each customer or suffer a fine of five times the commercial value of the missing stock. On the other hand the customers will buy additional stock (at commercial value) up to their capacity. Any stock exceeding capacity will be wasted. It will be your job to find a way to fill all the orders while maximizing profit. 2 Distribution Centers BRB has membership with a group of other foodstuff manufacturers. Together, the Mid-Atlantic Food and Drink Corp (MFDC) owns 6 distribution centers (DC) that are relevant to BRB. Instead of shipping products directly, BRB can ship larger quantities to any of these DCs who will handle final delivery. The cost of shipping from a DC to a customer behaves differently: BRB only pays a fraction of the cost proportional to the fraction of the weight capacity their products take up (assume that trucks from DCs are always loaded to capacity). See Table 6 for the coefficients. The cost of shipping to a DC is still fixed per truck (given in Table 5), but substantial savings are possible by shipping small amounts out of distribution centers. For example, if 15,000 tons are being shipped from DC 2 to Customer 4 then the cost of the whole truck is $109,000; but BRB for 34% of that cost. To be exact, they would pay $37,000. only pays 15,000 44,000 Table 5: Fixed cost (1000s of dollars per truck) to ship from BRB to each DC DC 1 429 DC 2 390 DC 3 429 Table 6: Proportional cost (1000s of dollars per truck) to ship from DCs to customers C 1 C 2 C3 C4 C 5 C6 C7 C 8 DC 1 388 546 410 415 124 160 306 160 DC 2 442 497 469 333 392 351 55 260 DC 3 315 237 233 292 160 115 192 242 DC 4 397 306 419 355 415 446 315 91 Find the configuration of shipments (via distribution centers) that maximizes total profit. Would you recommend this solution over those from part 1? Why? Again, your report should contain mathematical support for your recommendations, but should be well explained and legible to a non-engineer.