MANG1047 Seminar Questions
Week 8
As a group select the questions you think you will learn most by working on (you do not have to get through all of them!).
You can also work on questions from this week’s quizzes if you wish to.
1 A certain product sells for £10 a unit. The total cost of making and selling xunits of the product is given by cost=x2−20x+30
a) What is the fixed cost of production?
b) How is the profit related to the number of units produced?
c) What level of production will maximize the profit?
2 Find the value of x that minimizes the following expression:
2x2 − 4x + 20
3 Please answer the questions in a) and b)
a) In stock control problems, what are the main costs that make up the holding costs? Why are holding costs sometimes given in terms of an interest rate?
b) An online music retailer sells a steady 50,000 CDs every month. Each CD costs £5 to buy from the manufacturer and each delivery from the manufacturer is charged at £1500. The cost of holding each CD by the retailer is 20p per month, and CDs are sold to the customers at £12 each together with a charge of £0.25 per CD for delivery (which exactly covers the delivery cost to the customer). What is the optimal number of CDs that the retailer should order at a time from the manufacturer? Use this value to determine the frequency of deliveries from the manufacturer and the retailer’s profit each month?