Valence Pharmaceuticals has three manufacturing facilities in the US where they produce an anticancer drug. The drug is shipped from the plants to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. The distribution centers, A, B, C, and D, each needs to receive 10 shipments per month. The distance (in miles) from each plant to each distribution center is shown in the following table: Distribution Center Plant A B D 1 900 1,400 400 700 2 1,100 1,400 600 1,000 3 600 1,200 800 900 The freight cost for each shipment is $1.00 per mile. (a) Draw a network diagram representing the problem. Let xij be the number of shipments to make from plant i to distribution center j for i = 1, 2, 3 and j = a, b, c, d. (b) Formulate a linear optimization model that can be used to determine the shipping plan that will minimize total distribution costs. Be sure to define your decision variables, state the objective Zoom le function, and include all constraints label the constraint types. (Remember that to formulate a model means to write it out mathematically. Do not set up your model in Excel.) (c) Is the capacity of the plants equal to the demand at the distribution centers? Valence Pharmaceuticals has three manufacturing facilities in the US where they produce an anticancer drug. The drug is shipped from the plants to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. The distribution centers, A, B, C, and D, each needs to receive 10 shipments per month. The distance (in miles) from each plant to each distribution center is shown in the following table: Distribution Center Plant A B D 1 900 1,400 400 700 2 1,100 1,400 600 1,000 3 600 1,200 800 900 The freight cost for each shipment is $1.00 per mile. (a) Draw a network diagram representing the problem. Let xij be the number of shipments to make from plant i to distribution center j for i = 1, 2, 3 and j = a, b, c, d. (b) Formulate a linear optimization model that can be used to determine the shipping plan that will minimize total distribution costs. Be sure to define your decision variables, state the objective Zoom le function, and include all constraints label the constraint types. (Remember that to formulate a model means to write it out mathematically. Do not set up your model in Excel.) (c) Is the capacity of the plants equal to the demand at the distribution centers