Your company is working on developing a new mounting system for solar panels. You want to design the mounts to hold the load of the panel safely $($without failing$)$ while having the lowest energy payback time $($time needed for the energy produced by the system to be greater than the energy costs to produce the components of the system$).$ Assume the mounting system is composed of ties loaded in tension and the solar panels are of a fixed size $($fixed tie length$).$

Hint: Energy payback time $=($total embodied energy$)/($energy production rate$).$ You can leave the "energy production rate" as an arbitrary constant $($not dependent on material$).$

a$)$ What would be the output of the Translation phase for this design

b$)$ What is the material index for this design problem?

c$)$ Using the plot below, what are the three top materials for this design? What would be the worst material in the plot to use?

d$)$ A coworker suggests that you use oak as the material because it has the lowest embodied energy. How would you justify to your superiors that this either is or is not the best solution? $($Write one or two sentences explaining the selection$)$