1. Modelling
Mathematical Models
Put into Excel Spreadsheets

2. Modelling ideas
Input Variables
Decision Variables
Targets

3. First Maths Profit = Revenue - Cost Linear Cost: Linear Revenue
Cost = Fixed Cost + N* Variable Cost
Linear Revenue
Revenue = N* Price
Piecewise Linear Revenue
Revenue = N1*Price1 + N2*Price2 + …
(e.g. when you can sell some t-shirts at a premium)

4. Dealing with uncertainty Projections using falling value of money
Projected Costs
Dealing with uncertainty
(actually still to come in lecture)
Projections using falling value of money
100 pounds now is worth more than the promise of 100 pounds next year
Break-even analyses

5. Spreadsheets Absolute and relative addresses If statements Range names
Making one-way tables
Two-way tables
Goal Seek

6. Uncertainty Sam’s Bookshop Sam does not know how many books to order.
They are cheaper the more he orders
He has to sell them cheaply if he does not sell them quickly
He does not know how many he can sell

7. They are cheaper the more he orders
First 1000 books are 24 dollars each; next etc.
Use a Vertical Lookup Table

9. Uncertain Sales

10. Expected Value
Suppose somebody throws a dice and gives you a pound for each dot on the side that comes up
E.g. if a 4 is thrown you get 4 pounds
How much money can you expect to get on average?

11. Well there is a 1 in 6 chance of getting one pound + a 1 in 6 chance of getting 2 pounds etc.
1/6 (1) + 1/6 (2) + … + 1/6 (6)
= 3.5 pounds

12. Back to Sam Want to maximise Profit Profit =Revenue-Cost
Revenue =Units_sold_at_regular_price*Regular_price+
Units_sold_at_leftover_price*Leftover_price

13. Units_sold_at_leftover_price =
Order - Units_sold_at_regular_price
Units_sold_at_regular_price =
MIN(Order_quantity,Demand)
= IF(Order_quantity < Demand, Order_quantity,Demand)

14. Cost =VLOOKUP (Order_quantity,CostLookup,2)

16. Make a Table

17. For each line of the table we can compute an expected value of profit by multiplying the profits by the demand probailities and adding

18. Expected profit for order of 2000 is:
.025* *40,000 + ….