Question

5. A television company ships televisions from three warehouses to three retail stores on a monthly basis. Each warehouse has a fixed supply per month, and each store has a fixed demand per month. The manufacturer wants to know the number of television sets to ship from each warehouse to each store in order to minimize the total cost of transportation. Each warehouse has the following supply of televisions available for shipment per month: Warehouse Supply (member of sets) 1. Cincinnati 300 2. Atlanta 200 3. Pittsburgh 200 Total | 700 Each retail store has the following monthly demand for television sets: Store A New York B. Dallas C. Detroit Total Demand number of sets) 150 250 600 Costs of transporting the sets from the warehouses to the retail stores vary as a result of differences in modes of transportation and distances. The shipping costs per television set for each route is as follows: To Store norske From Warehouse А ТВ $16S $18 $14 $12 $13 S15 Formulate a standard linear programming model, using the correct terminology. (No solution is required.)

Answer 1

Let X_jk be the units transported from the warehouse-j to store-k for j=1,2,3 and k=A, B, C

Min Z = 16 X_1A + 18 X_1B + 11 X_1C + 14 X_2A + 12 X_2B + 13 X_2C + 13 X_3A + 15 X_3B + 17 X_3C

Subject to,

X_1A + X_1B + X_1C <= 300 [Capacity constraint for warehouse-1]
X_2A + X_2B + X_2C <= 200 [Capacity constraint for warehouse-2]
X_3A + X_3B + X_3C <= 200 [Capacity constraint for warehouse-3]

X_1A + X_2A + X_3A = 150 [Demand constraint for store-A]
X_1B + X_2B + X_3B = 250 [Demand constraint for store-B]
X_1C + X_2C + X_3C = 200 [Demand constraint for store-C]

X_jk >= 0 for j=1,2,3 and k=A, B, C