A snack food producer runs four different plants that supply product to four different regional distribution centers
The division operations manager is focused on one product, so he creates a table showing each plant's monthly capacity and each distribution center's monthly demand (both amounts in cases) for the product. The division manager supplements this table with the cost data to ship one case from each plant to each distribution center. Formulate an objective function and constraints that will solve this problem using linear programming.
Center 1 Center 2 Center 3 Center 4 Monthly Capacity
Plant A $2 $7 $5 $4 8000
Plant B $9 $4 $7 $6 12000
Plant C $7 $6 $4 $3 7500
Plant D $4 $8 $3 $5 5000
Monthly Demand 9000 8500 8000 7000
This is a cost minimization problem with 16 decision variables, one for each combination of plant and center; there are 8 constraints, one for each plant's capacity and one for each center's demand.
Objective Min Z = $2xA1 + $7xA2 + $5xA3 + $4xA4 + $9xB1 + $4xB2 + $7xB3 + $6xB4 + $7xC1 + $6xC2 + $4xC3 + $3xC4 + $4xD1 + $8xD2 + $3xD3 + $5xD4
Subject to
Plant A: xA1 + xA2 + xA3 + xA4 = 8000
Plant B: xB1 + xB2 + xB3 + xB4 = 12000
Plant C: xC1 + xC2 + xC3 + xC4 = 7500
Plant D: xD1 + xD2 + xD3 + xD4 = 5000
Center 1: xA1 + xB1 + xC1 + xD1 = 9000
Center 2: xA2 + xB2 + xC2 + xD2 = 8500
Center 3: xA3 + xB3 + xC3 + xD3 = 8000
Center 4: xA4 + xB4 + xC4 + xD4 = 7000
The optimal solution is:
Center 1 Center 2 Center 3 Center 4 Monthly Capacity
Plant A 8,000 8,000
Plant B 8,500 3,500 12,000
Plant C 500 7,000 7,500
Plant D 1,000 4,000 5,000
Monthly Demand 9,000 8,500 8,000 7,000 $113,500
You might also like to view...
The What Went Wrong feature in Chapter 15 focuses on Curves International, the fitness center for women. Since 2006 Curves has closed more than 4,000 locations
Which of the following reasons was not identified in the feature as one of the possible explanations for why so many Curves centers have closed? A) An inability to find enough potential franchisees B) The poor economy C) Cheaper competition D) The company failed to keep up with changing trends, including more flexible hours for busy working women. E) The company sold too many franchises that are located too close together.
The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?
A) 99 B) cannot be determined C) 78 D) 70.5