In determining the profit contribution the management did not deduct the labor cost because they are fixed costs. However, we could schedule over time in each of the three departments. The maximum available overtime are as follows: 300 hours in dept-1, 220 hours in dept-2, 250 hours in dept-3 and 200 hours in dept-4. The labor rate for overtime is $18/hour in department 1, $24/hour in department 2, $15/hour in department 3, and $21/hour in department 4.
Formulate a LP model to maximize profit. Don’t ignore the availability of overtime and the associated costs.
What are the production schedule and the profit? Type the answers in the space provided.
Attach the computer output. Make sure it is formatted neatly, as otherwise you will lose points for sloppy presentation
(Hint: This problem is similar to golf bag problem. However, there is a twist – availability of over time that comes with a cost associated. To handle these kinds of problem, you would create additional decision variables to help you decide the OT to be scheduled in the four departments. We can do that with four variables, call them T1, T2, T3 and T4, representing the OT for the 4 departments. So your right hand side of the constraint will change – it will be the regular time plus over time. As an example, for department 1, the time available will be 2,500 hours plus T1. Watch for the proper units in time. Also, don’t forget to adjust your objective function profit by the money paid for OT.
3) Baldwin Wooster Corporation
Baldwin Wooster Company manufactures tractors. Currently it has two plants located in Berea and Phoenix, with capacities of 50,000 and 70,000. The tractors are shipped to following distribution centers showing associated demand. Boston – 50,000, Dallas – 70,000, Orlando – 40,000 and Portland – 80,000,
Because of anticipated increase in needs for the tractors, Baldwin is considering opening one to three new plants. Cities being considered are Atlanta, Omaha, and Tampa with capacities of plant capacities of 90,000, 60,000 and 70,000 respectively. Annual fixed and operating costs (in $000) associated with the new locations are: Atlanta $2,900, Omaha $1,400, & Tampa $2,200. Shipping cost per tractor is shown in the table below.
Shipping Cost $/tractor
Plant Boston Dallas Orlando Portland
Berea $25 $30 $33 $45
Phoenix $50 $22 $52 $18
Atlanta $26 $32 $15 $47
Omaha $38 $20 $45 $35
Tampa $24 $36 $12 $45
Develop an optimal distribution system. This problem is similar to the problem in the test.
Type the answers below in the space provided. What are the optimal schedule and the optimal cost? Where would you build the new plant(s)?
