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Q7. (a) The daily profit, P pounds, of a small oil refinery is given by:

P = 80x - 0.2x², where x is the number of barrels of oil refined.

Calculate EACH of the following:

(i) the number of barrels to be refined to maximise the profit; (6)

(ii) the maximum profit. (2)

(b) Given: T = 3 + 4sin θ - 2cos θ

(i) Determine the value of dT/dθ when θ = 5π/6 radians    (4)

(ii) Solve dT/dθ = 0 for θ in the range π/2 ≤ θ ≤ π           (4)