The following curve was generated based on the proctor compaction test in the laboratory on soil samples from a field. Specifications call for the compacted unit weight to be at least $90\%$ of the Standard Proctor Maximum. When you excavated a sample of the soil from the field, it had a volume of $0\mathrm{.}045f{t}^3.$ The soil sample weighed $5lb$ wet and $4lb$ dry.

a$)$ Determine optimum moisture content.

b$)$ What is the field moisture content?

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c$)$ What is the field compacted dry unit weight $($in units of $l\frac{b}{f}{t}^3)?$

d$)$ What is the relative compaction $R($as a percentage$)?$