Background. You are excavating a $100$ ft long x $4$ ft wide x $10$ ft deep utility trench. The soil is a cohesive silty loam with an unconfined compressive strength $q_u=2ksf.$ You plan to use shoring constructed of upright sheeting and hydraulic bracing as shown. The hydraulic cylinders are $5$ feet apart horizontally. Your company already owns the shoring material. You estimate that it will cost $$225$ in labor to install it$.$

Design the same $10$ foot deep trench as a sloped excavation with no bracing following OSHA guidelines.

a$.$ What OSHA soil type is this? Explain.

b$.$ Is benching allowed for this soil type? Explain.

c$.$ Sketch the required trench cross section without benching. Label vertical and horizontal extents of the excavation and label the slope of the sides.

For the trench above:

a$.$ What volume of excavation is required for the shored solution?

b$.$ What volume of excavation is required for the sloped solution?

c$.$ The cost for excavation, backfill and compaction is $$\frac{2\mathrm{.}50}{?}$ bcy$.$ Is it cheaper to install shoring or to slope the excavation $($disregard time impacts$)?$I need detailed answer with clear calculations.