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Problem 3 (Distribution Network): The business scenario is presented as follows. The Sentry Lock Corporation manufacturers a popular commercial security lock at plants in Louisville, Detroit and Phoenix. The per unit cost of production at each plant is $35.50. $39.00. and $36.25, respectively. and the annual production capacity at each plant is 18,000,13,000, and 12,000, respectively. Sentry's locks are sold to retailers: through wholesale distributors in four cities across the United States. The unit cost of shipping from each plant to each distributor is summarized in the following table along with the forecasted demand from each distributor for the coming year. Sentry wants to determine the least expensive way of manufacturing and shipping locks from their plants to the distributor. Because the total demand from distributors exceeds the total production capacity of all plants. Sentry realized it will not be able to satisfy all the demand for its product. but wants to make sure each distributor will have the opportunity to fill at least 80% of the orders they receive, Create a spreadsheet model for this problem and solve it. What is the optimal solution? What is the optimal value? (a) Following the distribution network problem discussed in our lectures, draw a distribution netwo based on the information given above and label as much information as possible on the network th. you draw, including the unit shipping cost, demand from each destination. (b) Formulate this problem as a linear programming model. You should formulate the proble algebraically. Clearly define the decision variables and their units. Express the objective function an the constraints as linear functions of the decision variables that you define. You should also identii each constraint by attaching a short descriptive label to it (e.g., Boston Demand, or Louisville Capacit etc.). (Hint: In terms of the production capacity at each plant, you may assume that it is either full utilized or only used sufficiently to meet the minimum demand at each distributor.)

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