Question $4.$ A technology company is setting up a customer service center to handle technical support calls for their products. The company offers four main products, labeled as $x,Y,Z,$ and $W.$ The customer service representatives are trained to provide support for all products.

The expected average call handling time for each product's support is different:

$15$ minutes for product $x,$

$10$ minutes for product $Y,$

$20$ minutes for product $Z,$ and

$25$ minutes for product $W.$

The company projects to receive an average of:

$80$ calls per week for product $x,$

$120$ calls for product $Y,$

$60$ calls for product Z$,$ and

$40$ calls for product $W.$

The customer service center will be open six days a week, Monday through Saturday, and each representative will work five $8-$hour shifts per week. On average, each representative is expected to spend $5\mathrm{.}5$ hours on calls daily, with the remaining time allocated to breaks, training, and administrative tasks. How many customer service representatives should the company hire?