PLEASE SOLVE ONLY QE and QF

Part B – NON-LINEAR/EXTREMUM

Total for Part A: 35%

A London-based furniture maker produces a quantity (q) of 6 units of cabinets per week. The costs of the furniture maker are highlighted by the following equations:

•  Company's total fixed cost (FC) = £120

•  Total variable cost (VC) = -8q + 12q2

•  Demand for the units: 200 - 15q

  Required:

(a) Find the equation for the London furniture maker’s profit (3 marks)

2. (b) Set up a demand, cost and profit table using values across the range of ‘q’ for q =

   0,1, 2, 3, 4, 5, 6.

   (5 marks)

3. (c) Use the values from the table as coordinates in order to draw a demand, cost and profit graph. Explain what is happening with your 3 graphs.

   (12 marks)

4. (d) From your graph, differentiate your profit equation to find the value of ‘q’ which maximises the profit.

   (5 marks)

The London furniture maker has a sister company in the Liverpool with the following profit equation:
Profit = TR – TC = (200q -5q2) – (150 – 25q + Xq2)
Where X is unknown and q (Liverpool) = 7

(e) Find the value for ‘X’ coefficient based on q (Liverpool). (5 marks)

(f) Discuss the strong and weak points in the London and Liverpool models that are identified by sensitivity analysis. For example, suppose the q for London and/or

Liverpool Company was 3 units less (or 1 unit more). What would be the effects on the demand, cost and profit graphs?
Also, provide any other information that would enable the London and Liverpool branches to become more competitive in the furniture manufacturing markets.

PLEASE SOLVE ONLY QE and QF

 

a) b) q 0 1 2 3 4 5 6 Find the equation for the London furniture manufacturer's profit Demand: 200-15q Revenue: 200q - 15q(demand * q) Total cost: Profit: Set up a demand, cost and profit table Demand 200-15q 200 185 170 155 140 125 120-8q+12q 200q-15q2120+8q-12q -27q+208q-120 110 Cost 120-8q+12q 120 124 152 204 280 380 504 Profit 200q-15q2-120+8q-12q -120 61 188 261 280 245 156