Chapter 15, Problem 11P

You are asked to design a covered conical pit to store $50{\text{m}}^3$ of waste liquid. Assume excavation costs at $\$100/{\text{m}}^3$, side lining costs at $\$50/{\text{m}}^2$, and cover cost at $25/{\text{m}}^2$. Determine the dimensions of the pit that minimize cost (a) if the side slope is unconstrained and (b) if the side slope must be less than $45°$.