The Audiofile Company has decided to subcontract out the production of the speak

Question

The Audiofile Company has decided to subcontract out the production of the speakers needed for the poomoo vendors are available to supply the speakers. Each shipment would go to one of the company's two warehou shipping costs and the production quantity of each vendor are as shown in the table below. Vendor Warehouse 1 Warehouse 2 Production $3355 $129 $220 $100 enever one of the company's two factories needs a shipment of sneakers to assemble into the boomboxes, the company hires a trucker to bring the shipment in from one of the warehouses. The cost per shipment is given next, along with the number of shipments needed per month at each factory Unit Shipping Cost Factory 1 Factory 2 Warehouse 5700 $200 Warehouse 2 400 500 Monthly demand 10 Each vendor is only able to send a maximum of three shipments per month to each warehouse, and each warehouse is only able to send a maximum of six shipments per month to each factory. a) [10 points) Draw a network that depicts the company's transportation network. Identify the supply npdestransshipment -- Ganodes, and den and nodes in this network. Szzu (31 5200 TO tol 6200 163 V 235 737 67 229 . (V) 129031 (6 7 20-031 ( V TC37 t-61 tml b) [10 points) Formulate a network model for this problem. 33 3 Net cast of are V, - w, '234 vi - W2 - 33 V2 - W EL Vr-W, V3-W, V3-W Wi-F wy-Fr - wz FT

Explanation / Answer

Part (a) that you have done is correct. I will help you with part (b).

Whenever, you formulate such a problem, remember 3 things:

1. Objective function (maximization or minimization)

2. Constraints.

3. Decision Variables.

Here, objective must be to minimize the total cost of transporation.

Here, decision variables are the quantity to be transported along each route. So, decision variables are:

X(v1,w1), X(v1,w2), X(v2,w1), X(v2,w2), X(v3,w1), X(v3,w2), X(w1,f1), X(w1,f2), X(w2,f1), X(w2,f2)

where, X(v1,w1) = quantity shipped along the route V1 --> W1 and other variables are likewise.

1. Objective Function: Minimize Z = 234*X(v1,w1) + 335*X(v1,w2) + 229*X(v2,w1) + 129*X(v2,w2) + 220*X(v3,w1) + 100*X(v3,w2) + 200*X(w1,f1) + 700*X(w1,f2) + 400*X(w2,f1) + 500*X(w2,f2)

2. Constraints:

a. Net Flow Constraints: Net flow from each node -

-5 + X(v1,w1) + X(v1,w2) = 0 [At Node V1]

-5 + X(v2,w1) + X(v2,w2) = 0 [At Node V2]

-6 + X(v3,w1) + X(v3,w2) = 0 [At Node V3]

- X(v1,w1) - X(v2,w1) - X(v3,w1) + X(w1,f1) + X(w1,f2) = 0 [At Node W1]

- X(v1,w2) - X(v2,w2) - X(v3,w2) + X(w2,f1) + X(w2,f2) = 0 [At Node W2]

- X(w1,f1) - X(w2,f1) + 10 = 0 [At Node F1]

- X(w1,f2) - X(w2,f2) + 10 = 0 [At Node F2]

b. Capacity Constraints:

X(v1,w1), X(v1,w2), X(v2,w1), X(v2,w2), X(v3,w1), X(v3,w2) <= 3

X(w1,f1), X(w1,f2), X(w2,f1), X(w2,f2) <= 6

c. Non-negative constraints:

X(v1,w1), X(v1,w2), X(v2,w1), X(v2,w2), X(v3,w1), X(v3,w2), X(w1,f1), X(w1,f2), X(w2,f1), X(w2,f2) >= 0

This is the complete formulation. Please try to formulate all such problems as nodes and routes with decision variables as the quantitites along the routes and constraints as required.

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