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Modelling Mathematical Models Put into Excel Spreadsheets

Modelling Mathematical Models Put into Excel Spreadsheets. Modelling ideas. Input Variables Decision Variables Targets. First Maths Profit = Revenue - Cost Linear Cost: Cost = Fixed Cost + N* Variable Cost Linear Revenue Revenue = N* Price Piecewise Linear Revenue

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Modelling Mathematical Models Put into Excel Spreadsheets

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  1. Modelling • Mathematical Models • Put into Excel Spreadsheets

  2. Modelling ideas • Input Variables • Decision Variables • Targets

  3. First Maths • Profit = Revenue - Cost • Linear Cost: • 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. 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 1000 23 etc. • Use a Vertical Lookup Table

  8. Uncertain Sales

  9. 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?

  10. 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

  11. 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

  12. 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)

  13. Cost =VLOOKUP (Order_quantity,CostLookup,2) * Order_quantity

  14. Make a Table

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

  16. Expected profit for order of 2000 is: .025*30000 + .05*40,000 + ….

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