Problem $1.(100$ points$).$ Please be very CONCISE and Clear

One of the most effective strategy often implemented by Zara is the so$-$called postponement.

This strategy is often considered as the main element that justifies the success of the fast fashion business model. The next problem tries to illustrate the value of postponement.

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Yeah Inc. is a Canadian wholesaler of brightly colored T$-$Shirts. Yeah orders the T$-$shirts from

a manufacturer in Bangladesh. The lead time is $6$ months and the selling season is $4$ months.

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A$.$ The unit values are: price, r $=$ $$2|$ wholesale price w $=$ $$1.$

B$.$ The T$-$shirts come in $4$ different colors where the demand for one color is independent from the demand of another color

C$.$ The demand distribution is considered normal

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Color

Average Demand $($units$)$

Standard Deviation $($units$)$

Salvage Value

$($$$)$

Orange

$800$

$300$

$0\mathrm{.}75$

yellow

$300$

$170$

$0\mathrm{.}8$

Lime Green

$600$

$200$

$0\mathrm{.}7$

Signal Red

$400$

$130$

$0\mathrm{.}75$

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What are the optimal order quantities for the different colors?

What is the resulting expected profit?

A local dying company, Pink Ink inc. Contact Yeah.com and suggests that they postpone the

application of the color for an increase in the wholesale price by $10\%$

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This change involves buying uncolored $($known as greige$)$ T$-$shirts from Bangladesh.

Pink Inc. offers to color these T$-$shirts with a lead time of $3$ days, implying that they

can be colored to order.

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What is the benefit in general of postponement $($give a qualitative answer$)?$

Using this postponement strategy how many uncolored T$-$Shirts should yeah order?

What is the expected profit?

What is your final recommendation to Yeah?

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