Sharon Glessing, controller for Janson Company, has noticed that the company faces a $75$ percent learning rate for its specialty design line. In planning the cost of the latest design, Sharon assumed that the first set of units would take $1,000$ direct labor hours. She decided to use this information in budgeting for the cost of the total project, which would involve the manufacture of $16$ sets. Direct labor is paid $$40$ per hour.

Required:

$1.$ Complete the table below showing results by row for total production of: one unit, two units, four units, eight units, and sixteen units. $($Round hour answers to two significant digits.$)($Round Cumulative Total Time answers to the nearest whole number.$)$

Cumulative Number

of Units Cumulative Average Time

per Unit in Hours Cumulative Total Time:

Labor Hours

$1$ fill in the blank $1$

$1,000$

fill in the blank $2$

$1,000$

$2$ fill in the blank $3$

$750$

fill in the blank $4$

$1,500$

$4$ fill in the blank $5$

$562\mathrm{.}5$

fill in the blank $6$

$2,250$

$8$ fill in the blank $7$

$421\mathrm{.}88$

fill in the blank $8$

$3,375$

$16$ fill in the blank $9$

$316\mathrm{.}41$

fill in the blank $10$

$5,063$

$2.$ What is the total labor cost if Janson Company makes eight sets? Sixteen sets? $($Use the rounded answers in the subsequent computations$).$

Total labor cost for eight sets $fill in the blank $11$

$135,000$

Total labor cost for sixteen sets $fill in the blank $12$

$202,520$

$3.$ Using the logarithmic function, complete the table below showing results by row for each of unit sets one through eight. $($Round hour answers to two significant digits.$)($Round Cumulative Total Time and Time for Last Unit answers to the nearest whole number.$)$

Cumulative Number

of Units Cumulative Average Time

per Unit in Hours Cumulative Total Time:

Labor Hours Time for

Last Unit

$1$ fill in the blank $13$

$1,000$

fill in the blank $14$

$1,000$

fill in the blank $15$

$1,000$

$2$ fill in the blank $16$

$750$

fill in the blank $17$

$1,500$

fill in the blank $18$

$500$

$3$ fill in the blank $19$

fill in the blank $20$

fill in the blank $21$

$4$ fill in the blank $22$

$562\mathrm{.}5$

fill in the blank $23$

$2,250$

fill in the blank $24$

$5$ fill in the blank $25$

fill in the blank $26$

fill in the blank $27$

$6$ fill in the blank $28$

fill in the blank $29$

fill in the blank $30$

$7$ fill in the blank $31$

fill in the blank $32$

fill in the blank $33$

$8$ fill in the blank $34$

$421\mathrm{.}88$

fill in the blank $35$

$3,375$

fill in the blank $36$

What is the direct labor cost for the eighth set?

$fill in the blank $37$