Q1. Based on past experience, a chemicals firm estimates that the cost of new capacity additions obeys the law where is measured in tons per year and in millions of dollars. Demand is growing at the rate of 3,000 tons per year, and the accounting department recommends a rate of 12 percent per year for discounting future costs.
(a) Determine the optimal timing of plant additions and the optimal size of each addition.
(b) What is the cost of each addition?
Q2. A coordinate system is superimposed on a map. Three existing facilities are located at (5,15), (10, 20), and (6,9). Compute both the rectilinear and the Euclidean distances separating each facility from a new facility located at .
Q3. An industrial park consists of 16 buildings. The corporations in the park are sharing the cost of construction and maintenance for a new first-aid center. Because of the park’s layout, distances between buildings are most closely approximated by a rectilinear distance measure. Weights for the buildings are determined based on the frequency of accidents. Find the optimal location of the first-aid center to minimize the weighted sum of the rectilinear distances to the 16 buildings. A white paper with numbers and letters AI-generated content may be incorrect.
Q4. Consider Example 6.7 of the Pear Company in the lecture note (Example 7.7 in the textbook) assuming the following supplies and demands.
A close up of a paper AI-generated content may be incorrect.
Formulate the problem as a linear program and use Excel’s Solver to determine the optimal solution.
Q5. Re-solve Example 6.9 in the lecture note (Example 7.9 in the textbook) assuming that the capacity of the vehicle is only 250 loaves of bread.
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