The ABC Company produces magnetic letters at three different plants which serves four separate markets. The companys
Question:
The ABC Company produces magnetic letters at three different plants which serves four separate markets. The company’s plants are located in New York, Chicago and Los Angeles. Product produced at the plants is sent to markets in Miami, Houston, Minneapolis and Portland. The quantity produced at each plant and the quantity demanded in each market is provided in Table 2.
The distance between each plant and market is given in Table 3. The cost of transporting a box is given by the function: Transportation Cost = 5 + 5*D, where D is the distances identified in Table 3.
Each box of magnetic letters sells for $400 and costs $150 to produce. The ABC Company wants to determine how much product to ship from each plant to each market to maximize profit.
a. Formulate this problem as a linear programming problem.
b. Implement a spreadsheet model in EXCEL to solve the LP. What is the optimal solution?
c. Can the problem be set-up as a cost minimization problem? If so, would the optimal quantities shipped to each market from each plant be different? Set-up the problem as a cost minimization problem if needed and resolve, otherwise explain.
A Survey of Mathematics with Applications
ISBN: 978-0134112107
10th edition
Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde