The Best-for-Less Corp. supplies its two retail outlets from its two plants. Plant A will be supplying 30 shipments next month. Plant B has not yet set its production schedule for next month but has the capacity to produce and ship any amount up to a maximum of 50 shipments. Retail outlet 1 has submitted its order for 40 shipments for next month. Retail outlet 2 needs a minimum of 25 shipments next month but would be happy to receive more. The production costs are the same at the two plants but the shipping costs differ. The shipping cost per shipment from each plant to each retail outlet is given below, along with a summary of the other data.
The distribution manager, Jennifer Lopez, now needs to develop a plan for how many shipments to send from each plant to each of the retail outlets next month. Her objective is to minimize the total shipping cost.

a. Identify the individual decisions that Jennifer needs to make. For each of these decisions, define a decision variable to represent the decision.
b. Write a mathematical expression for the total shipping cost in terms of the decision variables.
c. Write a mathematical expression for each of the constraints on what the values of the decision variables can be.
d. State a complete mathematical model for Jennifer's problem.
e. What do you think Jennifer's shipping plan should be? Explain your reasoning. Then express your shipping plan in terms of the decision variables.

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Unit Shipping Cost Retail Outlet 1 Retail Outlet 2 Supply = 30 shipments s 50 shipments Plant A Plant B $700 $400 $600 2 25 shipments Needed = 40 shipments %3D