Question $5.$ A high$-$end electronics retail company is opening a service center to handle repairs for its range of gadgets, such as smartphones, tablets, laptops, and desktops. The company has four main gadget categories that need servicing $-$ referred to as $G1,G2,G3,$ and G$4.$

The estimated average repair time provided by the technical team is:

$40$ minutes for $G1,$

$50$ minutes for $G2,$

$45$ minutes for $G3,$ and

$30$ minutes for G$4.$

The company expects to receive:

$90$ repairs per week for $G1,$

$70$ repairs for G$2,$

$80$ repairs for $G3,$ and

$100$ repairs for G$4.$

The service center will operate on weekdays only, Jrom Monday to Friday, and each technician will work an $8-$hour shift per day. However, it is assumed that technicians will actually spend an average of $6$ hours per day on repairs, with the remaining time allocated to parts inventory, administrative work, and customer consultations. Considering an absenteeism rate of $10\%$ for the technicians, how many technicians should the electronics service center employ?