3.The Roadnet Transport Company expanded its shipping capacity by purchasing 90

Question

3.The Roadnet Transport Company expanded its shipping capacity by purchasing 90 trailer trucks from a bankrupt competitor. The company subsequently located 30 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of these warehouses to terminals in St. Louis, Atlanta, and New York. Each truck is capable of making one shipment per week. The terminal managers have indicated their capacity for extra shipments. The manager at St. Louis can accommodate 40 additional trucks per week, the manager at Atianta can accommodate 60 additional trucks, and the manager at New York can accommodate 50 additional trucks. The company makes the following profit per truckload shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport Terminal Warehouse St. Louis Atlanta New York Charlotte Memphis Louisville $1,800 1,000 1.400 $2.100 700 800 $1,600 900 2.200 The company wants to know how many trucks to assign to each route (G.e, warehouse to terminal) to maximize profit. a. Formulate a linear programming model for this problem b. Solve the model by using the computer.

Explanation / Answer

a. Let the no. of trucks shipped from Charlotte to St. Louis, Atlanta and New York be c1,c2 and c3 respectively.

Let the no. of trucks shipped from Memphis to St. Louis, Atlanta and New York be m1,m2 and m3 respectively.

Let the no. of trucks shipped from Louisville to St. Louis, Atlanta and New York be s1,s2 and s3 respectively.

Thus the objective function = 1800c1+2100c2+1600c3+1000m1+700m2+900m3+1400s1+800s2+2200s3

Constraints:

1. c1+c2+c3=30

2. m1+m2+m3=30

3. s1+s2+s3=30

4. c1+m1+s1<=40

5. c2+m2+s2<=60

6. c3+m3+s3<=50

7. All variables >=0

b. Solving the above in excel, using the solver function, the following solution is obtained:

Thus the maximized profit is $159,000 and 30 trucks are shipped from Charlotte to Atlanta, 30 trucks are shipped from Memphis to St. Louis and 30 trucks are shipped from Louisville to Atlanta.

Terminal Warehouse St. Louis Atlanta New York Total Charlotte 0.00 30.00 0.00 30.00 Memphis 30.00 0.00 0.00 30.00 Louisville 0.00 0.00 30.00 30.00 Total 30.00 30.00 30.00 Formula Total profit 159,000.00 1800c1+2100c2+1600c3+1000m1+700m2+900m3+1400s1+800s2+2200s3 Constraints 30.00 = 30.00 c1+c2+c3=30 30.00 = 30.00 m1+m2+m3=30 30.00 = 30.00 s1+s2+s3=30 30.00 <= 40.00 c1+m1+s1<=40 30.00 <= 60.00 c2+m2+s2<=60 30.00 <= 50.00 c3+m3+s3<=50

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