(10 marks Question 3 Profit and Loss We now consider the cost of manufacturing the articles...

 

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(10 marks Question 3 Profit and Loss We now consider the cost of manufacturing the articles in Q2. Suppose that the relationship between price and demand is p-19-2d and that the cost £C thousand of manufacturing d thousand articles is given by C=10+3d. The revenue £R thousand accruing from selling d thousand articles is calculated by: Revenue Demand x Price i.e. R=dxp. The profit £N thousand from such sales is given by: Profit= Revenue - Cost of manufacturing i.e. N=R-C. (a) Use these definitions of revenue and profit to obtain quadratic expressions for R and N in terms of d. If the demand is 2500, find the profit. (12 marks) (b) Solve the equation N= 0, giving your answers to 3 decimal places. Hence find the range of values of d for which the company makes a profit and the corresponding article price range. If the profit is £12,500 what is the corresponding demand? (20 marks) (c) Using symmetry (or otherwise) find the maximum profit and the corresponding demand and price. (8 marks) (10 marks Question 3 Profit and Loss We now consider the cost of manufacturing the articles in Q2. Suppose that the relationship between price and demand is p-19-2d and that the cost £C thousand of manufacturing d thousand articles is given by C=10+3d. The revenue £R thousand accruing from selling d thousand articles is calculated by: Revenue Demand x Price i.e. R=dxp. The profit £N thousand from such sales is given by: Profit= Revenue - Cost of manufacturing i.e. N=R-C. (a) Use these definitions of revenue and profit to obtain quadratic expressions for R and N in terms of d. If the demand is 2500, find the profit. (12 marks) (b) Solve the equation N= 0, giving your answers to 3 decimal places. Hence find the range of values of d for which the company makes a profit and the corresponding article price range. If the profit is £12,500 what is the corresponding demand? (20 marks) (c) Using symmetry (or otherwise) find the maximum profit and the corresponding demand and price. (8 marks)

Answer rating: 100% (QA)

b b192d C 10 3d Revenue a Profit N N 0 Now where deman... View the full answer