# maths

A company is planning to manufacture and sell a new headphone set. After conducting extensive market surveys, the research department provide the following estimates: Marginal costs function: c^' (x)=RM(40+0.4x) where x is the quantity sold for the fixed cost of RM 600. At the price of RM 100, 30 units of headphones were sold and at the price of RM 60, 50 units of headphones were sold

(ii) Find the total cost function (4 marks)

(iii) Find the total revenue function (2 marks)

(iv) The level of production in which revenue is maximised (3 marks)

(v) The profit, price per unit, total revenue and total cost when total revenue is maximised. (4 marks)

(vi) Find the change in total revenue when production level increases from 20 units to 30 units. Interpret your results. (4 marks)

(vii) Find the profit function (3 marks)

(viii) The level of production in which profit is maximised. (3 marks)

(ix) The maximum profit, price per unit, total revenue and total cost when profit is maximised (4 marks)

(x) Find the change in total profit when production level increases from 30 units to 40 units. Interpret your results. (4 marks)

(xi) Find the break-even of the production level

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