3. A Utility company with 2 plants (15 points) Recall that in Unit 2 we also had

Question

3. A Utility company with 2 plants (15 points) Recall that in Unit 2 we also had the following extension of the above one-plant Utility Company problem Suppose that the Utility Company is considering the possibility of building a second (more efficient) plant. Specifically, the cost of its existing plant, now called Plant 1, and the cost of the new plant, now called Plant 2, are given below: Plant 1 10,050+50, Plant 2 5,000+ 20, where Q, and Q, denote the respective kilowatts produced at the respective plants Thus, Q = Q1+ Q2. What are the optimal production levels and optimal profit level? (a) Formulate as an algebraic optimization model. (Handwrite answer, 5 points) (b) Create Excel model using your model from part (a). (Hand in via Blackboard, 5 points) (c) Then solve for the optimal output levels and optimal profit. (Hand in via B 5 points)

Explanation / Answer

In general, a transportation problem is specified by the following information: 1 A set of m supply points from which a good is shipped. Supply point i can supply at most si units. In the Powerco example, m 3, s1 35, s2 50, and s3 40. 2 A set of n demand points to which the good is shipped. Demand point j must receive at least dj units of the shipped good. In the Powerco example, n 4, d1 45, d2 20, d3 30, and d4 30. 3 Each unit produced at supply point i and shipped to demand point j incurs a variable cost of cij. In the Powerco example, c12 6. Let xij number of units shipped from supply point i to demand point j then the general formulation of a transportation problem is min im

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