A manufacturing process has a learning curve with a learning rate of $80\%.$ The initial production

time for the first unit is $100$ hours. Calculate the following:

a$)$ The time required to produce the fifth unit.

b$)$ The cumulative time required to produce the first five units.

c$)$ The cumulative average time per unit for the first five units. $($Ans: $74\mathrm{.}76)$

d$)$ The expected time to produce the $10$th unit.

e$)$ The cumulative time required to produce the first $10$ units.

f$)$ The cumulative average time per unit for the first $10$ units. $($Ans: $63\mathrm{.}15)$