from pulp import LpMinimize, LpProblem, LpVariable, lpSum # Define the linear programming problem model = LpProblem(name="walsh_juice_company", sense=LpMinimize) # Define the decision variables x = LpVariable.dicts("x", ((i, j) for i in range(3) for j in range(4)), lowBound=0) y = LpVariable.dicts("y", ((j, k) for j in range(4) for k in range(3)), lowBound=0) # Supply from vineyards (in tons) vineyard_supply = [1400, 1100, 1700] # Processing capacity of plants (in tons) plant_capacity = [1200, 1100, 1400, 1400] # Product demand (in tons) product_demand = [1200, 900, 700] # Bottled Juice, Concentrate, Jelly # Transportation costs (per ton) transportation_cost = [ [850, 720, 910, 750], # New York to plants [970, 790, 1050, 880], # Pennsylvania to plants [900, 830, 780, 820] # Ohio to plants ] # Processing costs per product at each plant processing_cost = [ [2100, 4100, 2600], # Virginia [2350, 4300, 2300], # Michigan [2200, 3950, 2500], # Tennessee [1900, 3900, 2800] # Indiana ] # Input-output relations input_for_bottled_juice = 1 input_for_concentrate = 2 input_for_jelly = 1.5 # Objective function: Minimize total cost (transportation + processing costs) model += lpSum(transportation_cost[i][j] * x[(i, j)] for i in range(3) for j in range(4)) + \ lpSum(processing_cost[j][k] * y[(j, k)] for j in