$6.$ An analyst has estimated that there will be an $84$ percent learning curve for an

assembly operation. The first assembly takes $48$ min, and the standard time is set

at $6$ min.

a$.$ How long will it take the operator to reach the standard time?

b$.$ Unfortunately, the operator falls ill after the first week on the new assembly

operation and returns after one week. What will be estimated time for the

operator to reach standard time now?

$7.$ Find the direct labor costs for a batch order of $100$ pumps. As this is a new order,

some learning will be occurring during the assembly process. The first assembly

takes $50$ min, but the second one takes only $35$ min. The standard time is estimated

as $10\mathrm{.}0$ min. The base wage is $$10/$h$.$

a$.$ Find the equation for the learning curve for this assembly.

b$.$ How many cycles does it take a worker to reach the standard time of

$10\mathrm{.}0$ min?

c$.$ How long is the overall time to reach $10$ min?

d$.$ Assume that the operator continuously improves $($i$.$e$.,$ follows the learning

curve$).$ What are the direct labor costs for the total batch of $100$ pumps under

a day work plan? What are the direct labor costs for the total batch of $100$

pumps under a standard hour plan?

e$.$ What is the operator$$s performance $($in $\%)$ at the $100$th pump, if he or she

continues learning?

f$.$ What is the direct unit labor cost for the company for the last $(100$th$)$ pump

under the standard hour plan?