The Lugumi Machinery Company has been offered a contract to build and deliver nine extruding presses to the Homestead Bottling Company. The contract price is contingent on meeting a specified delivery time, a bonus being given for early delivery. The marketing department has been established the following cost and time information.
Activity
Normal time (weeks) Normal Crash Crash a B m Cost($) time Cost($)
1-2 1 5 3
2-3 1 7 4
2-4 1 5 3
2-5 5 11 8
3-6 2 6 4 4-6 5 7 6 5-7 4 6 5 6-7 1 5 3
(Weeks) 5,000 1 8,000 3 4,000 2 5,000 7 3,000 2 2,000 4 10,000 4 7,000 1
9,000 14,000 6,000 6,000 5,000 3,600 14,000 10,600
The normal delivery time is 16 weeks for a contract price of $ 62,000.
6
a)
Based on the calculated profitability for each specified delivery time below, recommend the delivery schedule that Lugumi Machinery Company should follow.
Contract Delivery Time(Weeks) 15
14
13
12
Contract Amount(USD) 62,500
65,000
70,000
72,500
b)
Based on the foregoing data, what are the chances of completing the contract sometime after the normal delivery time, say one week later?
To determine the profitability for each specified delivery time, we need to calculate the total cost for each delivery schedule.
For a contract delivery time of 15 weeks, the total cost is:
1-2 -> 1 week (normal time) -> $5,000
2-4 -> 2 weeks (normal time) -> $4,000
4-6 -> 5 weeks (normal time) -> $6,000
6-7 -> 1 week (normal time) -> $10,000
Total cost = $5,000 + $4,000 + $6,000 + $10,000 = $25,000
Contract amount = $62,000
Profitability = Contract amount - Total cost = $62,000 - $25,000 = $37,000
For a contract delivery time of 14 weeks, the total cost is:
1-2 -> 1 week (normal time) -> $5,000
2-3 -> 1 week (normal time) -> $8,000
3-6 -> 2 weeks (crash time) -> $3,600
6-7 -> 1 week (normal time) -> $10,000
Total cost = $5,000 + $8,000 + $3,600 + $10,000 = $26,600
Contract amount = $65,000
Profitability = Contract amount - Total cost = $65,000 - $26,600 = $38,400
For a contract delivery time of 13 weeks, the total cost is:
1-2 -> 1 week (normal time) -> $5,000
2-3 -> 1 week (normal time) -> $8,000
3-6 -> 2 weeks (crash time) -> $3,600
6-7 -> 1 week (normal time) -> $10,000
Total cost = $5,000 + $8,000 + $3,600 + $10,000 = $26,600
Contract amount = $70,000
Profitability = Contract amount - Total cost = $70,000 - $26,600 = $43,400
For a contract delivery time of 12 weeks, the total cost is:
1-2 -> 1 week (normal time) -> $5,000
2-3 -> 1 week (normal time) -> $8,000
3-6 -> 2 weeks (crash time) -> $3,600
6-7 -> 1 week (normal time) -> $10,000
Total cost = $5,000 + $8,000 + $3,600 + $10,000 = $26,600
Contract amount = $72,500
Profitability = Contract amount - Total cost = $72,500 - $26,600 = $45,900
Based on these calculations, Lugumi Machinery Company should follow the delivery schedule that results in the highest profitability. In this case, the recommended delivery schedule would be a contract delivery time of 12 weeks, with a contract amount of $72,500.
b) To determine the chances of completing the contract sometime after the normal delivery time (i.e. one week later), we need to analyze the crash times. From the given data, the crash times for activities 1-2, 4-6, and 6-7 are 5, 7, and 5 weeks respectively.
The normal delivery time is 16 weeks, so if the contract is completed one week later, the total time to complete the contract would be 17 weeks. We need to calculate the probability of completing all activities within this time frame.
Using the crash times, we can calculate the total crash time required for the specified delivery time:
1-2 (normal time) + 4-6 (crash time) + 6-7 (crash time) = 1 week + 2 weeks + 1 week = 4 weeks
Since the total crash time required is less than or equal to the specified delivery time, there is a high chance of completing the contract sometime after the normal delivery time, one week later.