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Q7. (a) Bar staff in a pub are paid £ 8 an hour. If the bar is understaffed the lost profit is £ {512/x} per hour, where x is the number of staff on duty. Determine the staffing level which will minimize the total staffing cost per hour. (8)

(b) Given P = 20 x - 50 sin⁡ (x, solve EACH of the following for x in the range 0 ≤ x  ≤  π):

(i) dP/dx = 0 ; (5)

(ii) (d² P)/(dx² ) = 0. (3)