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MN-2506 Academic Year 2024-25
MN-2506 Coursework: Maths for Business Assignment
Answer ALL questions.
Write ALL steps (workings) as you will be marked on methods and not just your final answer!
You need to name and write in full ALL rules used each and every time they are used (even in the
same question). Include All your workings including those carried out on the powers.
Question 1: [40 Marks]
(a) A local Swansea bakery specialises in customised cakes and pastries in Swansea. Due to growing
demand, the owners are analysing their cost and revenue functions to optimise production and
pricing. The bakery’s financial team has asked for your expertise in helping them calculate key
marginal functions to guide their pricing and output decisions given the following information:
(i) That the bakery’s total cost function is:
= 2
4 + 5
3 + 3
2 + 6 + 20 [2 Marks]
(ii) That the bakery’s total revenue function is (please use the product rule here):
= (3
2 + 8 5) + 7 [4 Marks]
(b) As the bakery is expanding its online order system and expects increased demand. To plan
effectively, they have asked you to calculate what the relevant marginal functions are based on
their new total cost and total revenue functions given below:
(i) = 7
3+ 2
2 + 5 + 8 [2 Marks]
(ii) = eQ(4
2 + 3 + 2) [4 Marks]
(c) The bakery has rolled out a new product and management wants you to:
(i) calculate the total profit function and use it to find the profit maximisation quantity for this
product given that:
TR = Q2 + 48Q and TC = Q2 + 12Q + 30
What is the profit at this quantity
[15 Marks]
(ii) Now use the other profit maximisation rule (MR=MC) to calculate the quantity at which
profit is maximised. [Hint: it should be the same as the quantity found using the total profit
function] [13 Marks]
MN-2506 Academic Year 2024-25
Question 2: [20 Marks]
For the following demand functions, work out what their respective elasticity of demand ( d) at a
price of 30:
(i) P = 50 – 5Q2
[5 marks]
(ii) P = 120 – 40Q2
[5 marks]
(iii) P = 90 – 3Q [5 marks]
(iv) Explain your findings [5 marks]
Question 3: [40 Marks]
A UK-based travel company operates a luxury coach service between major cities in Wales and
England. Due to rising fuel prices and maintenance costs, the company is considering increasing
ticket prices. However, they want to assess how this decision might impact consumer surplus and
producer surplus before making any pricing changes. The company’s market demand and supply
functions for one-way coach tickets is currently given by:
PD = 150 –2Q and PS = 50 + 4Q
Where P represents the ticket price in GBP (￡) and Q represents the number of coach tickets sold
daily.
(a) Find the market equilibrium where quantity demanded equals quantity supplied.
[6 marks]
(b) Calculate the consumer surplus at the equilibrium point using both integration and
geometry and illustrate your findings. Explain what consumer surplus represents in this
market context.
[12 marks]
(c) Calculate the producer surplus at market equilibrium using both integration and geometry
and illustrate your findings. Explain the significance of producer surplus for this company.
[12 marks]
(d) Suppose that due to the increased fuel costs and regulatory fees, the company’s cost
structure has changed, shifting the supply curve to PS = 70 + 4Q. Calculate the new market
equilibrium and use geometry to work out the new producer and consumer surpluses.
Illustrate your findings on a demand-supply plot and discuss how this shift affects both
consumers and producer. Give a recommendation to this company based on your analysis
and findings.
[10 marks]
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