Answer to Question #244509 in Math for Penny

Question

A company producing a household item has a fixed monthly cost of RM 900 and a variable cost of RM 9.70.

The price-demand equation for the production of LED television sets is given by, 𝑥=520−(16)𝑝

where 𝑥 is the number of sets that can be sold at a price RM 𝑝 per item.

(i) Express the price, 𝑝 as a function of the demand 𝑥. (1 mark)

(ii) Find the cost function, 𝐶(𝑥) and revenue function, 𝑅(𝑥). (2 marks)

(iii) Find the marginal revenue and marginal cost functions. (4 marks)

(iv) Find the profit function, 𝑃(𝑥). (2 marks)

(v) Find the output that gives maximum profit for the company. (1 mark)

(vi) Determine the maximum profit. (2 marks)

(vii) Find the output at break-even point. (5 marks)

(viii) Draw the graph for profit function, clearly showing the breakeven levels, and the maximum profit. (3 marks)

Answer 1

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