Nearly $$40$ billion of sofas and sofa sets are sold each year in the United States$1$

$.$ Making a sofa is a

complex multi$-$step process. Making one by hand can take between $200-$to$-300$ hours; however, a

modern factory can make a sofa every $10-$to$-15$ minutes. These reduced times are the result of

automation and optimized factory layout and line balancing. Below are basic diagrams of how sofas are

constructed.According to Koruca, Koker, Chehbi$-$Gamoura and Ulsik $(2018)2$

in a modern well$-$run factory dedicated

to manufacturing sofas, there are $32$ workstations with an average cycle $($Takt$)$ time of $601\mathrm{.}3$ seconds

$.$

Assume that each workstation has one worker. The average American factory worker makes $$15\mathrm{.}00.$ per hour, adding fringes, benefits and payroll taxes, the total hourly cost is $$20\mathrm{.}10$ per hour. In China

the average factory workers salary is $8,000$ Yuan per month

$,$ which comes to $$1,200$ per month, or an

hourly rate of $$6\mathrm{.}92.$ Including $20\%$ for employers$$ social security contribution $($health insurance,

maternity insurance, work related injury insurance and unemployment insurance$)$ the hourly cost of a

Chinese factory worker is $$8\mathrm{.}31$ per hour. The average cost to ship a container from China to the Port

of Los Angles is given in the table below$6$

$.$ Depending upon the size of the sofa, there are anywhere

from $8-$to$-18$ sofas per shipping container

Standard Container Shipping Cost from China to USA

Charge Low High

Factory to port $ $50$ $ $480$

Clearance $100300$

Shipping Shenzhen, China to LA$,$ CA$.$ USA $2,2302,460$

Insurance $(0\mathrm{.}2\%)818$

Port charges $100450$

Customs bond $100200$

Local Charges $100450$

A typical US furniture manufacturer sells $11,560$ sofas annually $($or approximately $32$ sofas per day$).$ It

spends $$175$ on raw and processed materials per sofa and sells sofas to furniture stores at an average

wholesale price of $$650,$ whether the sofas are made in the USA or China. This company is considering

outsourcing the sofas to a Chinese manufacturer. If the company decides to outsource, it will purchase

the sofas at an average price of $$289\mathrm{.}63$ FOB. Approximately $3\%$ of the sofas manufactured in the USA

are damaged in transit while, $8\%$ of sofas made in China are damaged in transit. $98\%$ of customers

backorder damaged sofas. The rehandling fees for damaged sofas are $$250$ each. The company would

be able to sell its production equipment for $$1\mathrm{.}2$ million and get rid of its factory for $$1\mathrm{.}6$ million; as

well as the overhead and expenses associate with the factory. The order cycle time for producing in

the USA is $4$ days, with a standard deviation of $1$ day. The order cycle time for producing in China is $14$

days with a standard deviation of $4$ days.

Answer question $3$

$(3)$ using an average of $12$

sofas per shipping container, calculate the average cost of shipping a sofa.