1. CASE 1: LEARNING
CURVE ANALYSIS
Group 7

2. Problem #1
The ABC Company has just been given the
following production schedule for ski-lift
gondola cars. This product is considerably
different from any others the company has
produced. Historically, the company‘s learning
rate has been 80% on large projects. The first
unit took 1,000 hours to produce.

3. Month Units Cumulative
1 3 3
2 7 10
3 10 20
4 12 32
5 4 36
6 2 38
a. Estimate how many hours would be
required to complete the 38th unit.

4. Solution
a) a. We use the learning curve formulas to
calculate the time required for the 38th unit:
a. Given: L=0.80 T1= 1000 hrs.
T38 = T1 (N (log L/log 2))
= 1000 (38 log 0.80/log 2)
= 310.04 hrs

5. • b. If the budget only provides for a maximum
of 30 direct labor employees in any month and
a total of 15,000 direct labor hours for the
entire schedule, will the budget be adequate?
Assume that each direct labor employee is
productive for 150 work hours each month.

6. Cumulative Hours
Mont
hs Units
Cummulative
Units
Cumulative
Average
Cumulative
Average Time per
Unit
Cumulative Total
Hours for all Units
1 3 3 0.834034568 834.034568 2502.103704
2 7 10 0.631537303 631.5373025 6315.373025
3 10 20 0.524247142 524.2471422 10484.94284
4 12 32 0.45870687 458.7068697 14678.61983
5 4 36 0.443285172 443.2851721 15958.26619
6 2 38 0.436342826 436.3428259 16581.02738

7. Number of hours per month.
Month
1 2502.103704 - 0 = 2502.103704 hrs
2 6315.373025-2502.103704= 3813.269321 hrs
3 10484.94284-6315.373025 = 4169.569815 hrs.
4 14678.61983-10484.94284= 4193.67699 hrs.
5 15958.26619-14678.61983= 1279.64636 hrs.
6 16581.02738-15958.26619= 622.76119 hrs.

8. Direct Labor Hours
Month Direct Labor Workers by Month
1 (2,502.1 hr)/(150 hr) = 16.7, or 17
2 (3,813.3 hr)/(150 hr) = 25.4, or 26
3 (4,169.6 hr)/(150 hr) = 27.8, or 28
4 (4,193.7 hr)/(150 hr) = 27.9, or 28
5 (1,279.7 hr)/(150 hr) = 8.5, or 9
6 (622.5 hr)/(150 hr) = 4.2, or 5

9. Conclusion:
*The schedule is sufficient in terms of the
maximum direct labor required in any month because
it never exceeds 30 employees. However, the total
cumulative hours are 16,581, which exceeds the
budgeted amount by 1,581 hours. Therefore, the
budget will not be adequate.

10. Problem 2
XYZ Company has $200,000 in cash, no inventory, and a 90
percent learning curve. To reduce the complexity of this problem, ignore
the hiring and training costs associated with dramatically increased
production. Employees are paid $20 per hour every Friday for that
week‘s work. XYZ has received an order to build 1,000 oak desks over
the next 15 weeks. Materials cost $400 per desk. Suppliers make
deliveries each Monday and insist on cash upon delivery. The first desk
takes 100 hours of direct labor to build. XYZ will be paid $1,500 per
desk two weeks after the desks are delivered. Should XYZ take this
order?
Additional Assumptions:
• Products are delivered at the end of each week.
Cash inflow from sales occurs at the end of the week.

11. Given: $ 20 per hour
100 hours per desk
$ 400 material cost per desk
$ 20 per hour x 100 hours per desk
= $ 2000 per desk
Cost:
$ 400 material cost per desk + $ 2000 per desk
= $ 2400 per desk

12. Week Units Total cost Inflows every after 2 weeks
1 2 4800
2 4 9600
3 8 19200 3000
4 12 28800 6000
5 14 33600 12000
6 24 57600 18000
7 64 153600 21000
8 128 307200 36000
9 128 307200 96000
10 128 307200 192000
11 88 211200 192000
12 100 240000 192000
13 100 240000 132000
14 100 240000 150000
15 100 240000 150000
150000
150000
Cash Outflows & Inflows

13. 350000
300000
250000
200000
150000
100000
50000
0
Cash Flow Chart
0 2 4 6 8 10 12 14 16
Values
Weeks
Total cost Inflows every after 2 weeks

14. Conclusion:
The company should not take the
order, because the total cost exceed the
cash inflow every after two weeks.