## Problems

18-1 When a learning curve is plotted on ordinary graph paper, the curve appears to level off. But when the curve is plotted on log-log paper, it appears that the improvements can go on forever. How do you account for the difference? Can the improvements occur indefinitely? If not, what factors could limit continuous improvement?

18-2 A company is performing on an 85 percent learning curve. If the first unit requires 620 hours, how much time will be required for the 300th unit?

18-3 A company working on a 75 percent learning curve has decided that the production standard should be 85 hours of production for the 100th unit. How much time should be required for the first unit? If the first unit requires more hours than you anticipated, does this mean that the learning curve is wrong?

18-4 A company has just received a contract for 700 units of a certain product. The pricing department has predicted that the first unit should require 2,250 hours. The pricing department believes that a 75 percent learning curve is justified. If the actual learning curve is 77 percent, how much money has the company lost? Assume that a fully burdened hour is \$65. What percentage error in total hours results from a 2 percent increase in learning curve percentage?

18-5 If the first unit of production requires 1,200 hours and the 150th unit requires 315 hours, then what learning curve is the company performing at?

18-6 A company has decided to bid on a follow-on contract for 500 units of a product. The company has already produced 2,000 units on a 75 percent learning curve. The 2000th unit requires 80 hours of production time. If a fully burdened hour is \$80 and the company wishes to generate a 12 percent profit, how much should be bid?

18-7 Referrring to question 18-6, how many units of the follow-on contract must be produced before a profit is realized?

18-8 A manufacturing company wishes to enter a new market. By the end of next year, the market leader will have produced 16,000 units on an 80 percent learning curve, and the year-end price is expected to be \$475/unit. Your manufacturing personnel tell you that the first unit will require \$7,150 to produce and, with the new technology you have developed, you should be able to perform at a 75 percent learning curve. How many units must you produce and sell over the next year in order to compete with the leader at \$475/unit at year end? Is your answer realistic, and what assumptions have you made?

18-9 Rylon Corporation is an assembler of electrical components. The company estimates that for the next year, the demand will be 800 units. The company is performing on an 80 percent learning curve. The company is considering purchasing some assembly machinery to accelerate the assembly time. Most assembly activities are 85-90 percent labor intensive. However, with the new machinery, the assembly activities will be only 25-45 percent labor intensive. If the company purchases and installs the new equipment, it will occur after the 200th unit is produced. Therefore, the remaining 600 units will be produced with the new equipment. The 200th unit will require 620 hours of assembly. However, the 201st unit will require only 400 hours of assembly but on a 90 percent learning curve.

a. Will the new machine shorten product assembly time for all 800 units and, if so, by how many hours?

b. If the company is burdened by \$70 per hour, and the new equipment is depreciated over five years, what is the most money that the company should pay for the new equipment? What assumptions have you made?