A gas station earns $2.60 in revenue for each gallon of regular gas it sells, $2.75 for each gallon of midgrade gas, and $2.90 for each gallon of premium gas. Let X₁, X₂, and X₃ denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that X₁, X₂, and X₃ have means μ₁ = 1500, μ₂ = 500, and μ₃ = 300, and standard deviations σ₁ = 180, σ₂ = 90, and σ₃ = 40, respectively.

a. Find the mean daily revenue.

b. Assuming X₁, X₂, and X₃ to be independent, find the standard deviation of the daily revenue.