You work for the food delivery service Food Bring. Deliveries are made from the trendy restaurant "Vertex R

$"$ to the luxurious apartment blocks known as vertices S$,$T$,$U$,$V$,$W$,$X$,$Y

and Z

$.$ Food Bring pays you a fixed price per delivery based on the chart below:

Destination vertex S

T

U

V

W

X

Y

Z

Dollars per delivery $35359999$

$($a$)$ Traffic conditions are terrible! You can$$t drive directly to some locations without driving past others, and your navigation app estimates that the journey between each pair of adjacent locations takes a certain amount of time $($in minutes$)$ indicated by the edge weights below.

Maple plot

What is the shortest travel time to each of the eight vertices?

Destination S

T

U

V

W

X

Y

Z

Travel time from Vertex R

$($minutes$)$

$4$

$11$

$6$

$8$

$7$

$14$

$8$

$10$

Syntax advice: Enter your answers as integers $($without units$).$

$($b$)$ Assuming that the shortest path is always taken, which delivery option offers the best hourly wage if we consider only the time it takes for a one$-$way trip from Vertex R

to the destination?