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Q7. (a) A company specializes in producing water pump control panels.

The cost of producing x control panels per day is £(x² + 50x + 15).

The selling price of each control panel £ (300 - 4x)

Use differential calculus to determine EACH of the following:

(i) the daily output for maximum profit;     (8)

(ii) the maximum daily profit;         (2)

(iii) the production cost of each panel when operating at maximum profit.      (2)

(b) Given T = 5 + 3cos q - 2sin q, calculate correct to 2 decimal places, the value of

dt/dq when q = 2p/3 radians.       (4)