Question $4$

"Elegant Creations" is a bespoke dressmaking shop established five years ago on the outskirts of Copenhagen. The shop is the brainchild of Alex and Jamie Taylor, a married couple who share a passion for fashion and design. With Alex's expertise in tailoring and Jamie's flair for design, they have created a unique brand known for its quality, elegance, and personal touch.

Since its inception, "Elegant Creations" has steadily built a reputation for delivering high$-$quality, custom$-$made dresses. The couple's dedication to their craft and their customers has fostered a loyal clientele. Recently, the shop experienced a significant upsurge in demand, attributed to glowing customer referrals and increased visibility from social media exposure. This surge has led to extended work hours, with a normal working day being $9$ hours and a growing backlog of orders.

The increase in demand, while a positive sign of the business's success, has placed a strain on the couple. Alex and Jamie are currently managing all aspects of the business, from client consultations to the final stitch. The workload has become unsustainable, leading to concerns about maintaining their high standards and managing customer expectations. The couple needs to make $150$ dresses in a normal $5-$day week.

To address this challenge, Alex and Jamie are contemplating hiring additional staff. They are considering employing skilled dressmakers to assist in the creation process, allowing them to maintain the quality of their work while meeting the increased demand. However, they are cautious about ensuring new employees share their commitment to craftsmanship and customer service. Additionally, they are exploring options to expand their workspace to accommodate a larger team without losing the intimate and personalized atmosphere that defines "Elegant Creations".

Answer the following:

$($a$)$ Using Little's Law, calculate how many dres$$makers Alex and Jamie need to employ to meet the weekly demand? $($Answers must show workings and be clearly legible.$)$

$($b$)$ Discuss the different types of layouts available to Elegant Creations to choose from if they wish to expand their workspace. Clearly outline the strengths and weaknesses of each layout type and the one you would recommend.