Question

# Wildcat Paper Mills, Inc., has two paper plants, one in Cincinnati and one in Syracuse. Warehouse...

Wildcat Paper Mills, Inc., has two paper plants, one in Cincinnati and one in Syracuse. Warehouse facilities are located in Albany and Erie. Distributors are located in Boston, New York City, and Philadelphia. Paper units manufactured at a plant must be shipped to a warehouse for inspection before they arrive at a distributor. Its management wants to find the optimal shipping arrangement that can lead to the minimal shipping cost that meets distributors' demands. The plant capacities and distributor demands for the next month are as follows:

 Plant Capacity (units) Cincinnati 300 Syracuse 275
 Distributor Demand (units) Boston 250 New York 125 Philadelphia 150

The unit transportation cost between any pair of locations is summarized below:

 Cincinnati Syracuse Albany Erie Boston New York City Cincinnati * Syracuse \$     4.25 * Albany \$     3.00 \$         2.50 * Erie \$     5.50 \$         2.75 \$ 2.70 * Boston \$     6.00 \$         2.25 \$ 3.25 \$ 0.75 * New York City \$     4.00 \$         1.45 \$ 1.25 \$ 5.55 \$ 6.25 * Philadelphia \$     2.15 \$         3.45 \$ 2.55 \$ 1.85 \$ 1.95 \$    2.05

Define the decision variables and use them to list the linear program for this problem.

Decision variables: Let Xij be the quantity to ship from origin node to destination node.

where, plants nodes {1,2}, warehouses nodes {3,4} and distributor nodes {5,6,7}

Linear program is following

Min 3X13+5.5X14+2.5X23+2.75X24+4.25(X12+X21)+2.7(X34+X43)+3.25X35+1.25X36+2.55X37+0.75X45+5.55X56+1.85X57+6.25(X56+X65)+1.95(X57+X75)+2.05(X67+X76)

s.t.

X12+X13+X14-X21 <= 300

X21+X23+x24-X12 <= 275

X13+X23+X43-X34-X35-X36-X37 = 0

X14+X24+X34-X43-X45-X46-X47 = 0

X35+X45+X65+X75-X56-X57 = 250

X36+X46+X56+X76-X65-X67 = 125

X37+X47+X57+X67-X75-X76 = 150

All variables >= 0

#### Earn Coins

Coins can be redeemed for fabulous gifts.