Pohlman Company makes aircraft engines. Pohlman has noticed that, in general, each new engine design is subject to an $80$ percent learning rate. Assume that the first unit produced takes $500$ hours, and direct labor is paid an average of $$45$ per hour.

Required:

$1.$ Set up a table with columns showing: the cumulative number of units, cumulative average time per unit in hours, and cumulative total time in hours. Show results by row for total production of: one engine, two engines, four engines, eight engines, sixteen engines, and thirty$-$two engines. $($Round hour answers to two decimal places.$)$

Cumulative Number of Units Cumulative Average Time per Unit in Hours Cumulative Total Time: Labor Hours

$1$ fill in the blank $1$

$500$

fill in the blank $2$

$500$

$2$ fill in the blank $3$

$400$

fill in the blank $4$

$800$

$4$ fill in the blank $5$

$320$

fill in the blank $6$

$1,280$

$8$ fill in the blank $7$

$256$

fill in the blank $8$

$2,048$

$16$ fill in the blank $9$

$204\mathrm{.}80$

fill in the blank $10$

$5,242\mathrm{.}88$

$32$ fill in the blank $11$

$163\mathrm{.}84$

fill in the blank $12$

$5,265\mathrm{.}04$

$2.$ What is the total labor cost if Pohlman manufactures the following number of engines: one, four, or sixteen?

Cost for manufacturing one engine $fill in the blank $13$

$22,500$

Cost for manufacturing four engines $fill in the blank $14$

$57,600$

Cost for manufacturing sixteen engines $fill in the blank $15$

$147,456$

What is the average cost per engine for the following number of engines: one, four, or sixteen? $($Round your answers to the nearest dollar.$)$

Average cost per system for one engine $fill in the blank $16$

$22,500$

Average cost per system for four engines $fill in the blank $17$

$13,725$

Average cost per system for sixteen engines $fill in the blank $18$

$9,257$

$3.$ What if Pohlman is preparing a bid to build $16$ engines? If necessary, round your answers to both parts to the nearest dollar.

Calculate budgeted labor cost for an engine design which Pohlman has built before $($assume that $16$ of these engines had been made previously and the first unit took $500$ hours$).$

$fill in the blank $19$

$148,110$

Calculate budgeted labor cost for a new engine design that Pohlman's workers have never made before $($assume the first unit will take $500$ hours$).$

$fill in the blank $20$

$148,110$

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