$23$;$24$;$25$

$2024$

POE: Question $1$ Modelling and Solving Decision$-$making Problems in a Spreadsheet$\_($Marks: $25)$

Suppose you and your friend run a small bicycle shop called "Friends Bicycle". You and your friend must order bicycles for the coming season. Orders for the bicycles must be placed in quantities of $10.$ The cost per bicycle is R$350$ if you and your friend order $10,$ R$335$ if you and your friend order $20,$ R$325$ if you and your friend order $30,$ and R$320$ if you and your friend order $40.$ The bicycles will be sold for R$500$ each. friend run out of bicycles during the season, then you and your friend will suffer a loss of "goodwill" among your customers. You and your friend estimate this goodwill loss to be R$25$ per customer who was unable to buy a bicycle. You and your friend estimate that the demand for bicycles this season will be $5,15,25,$ or $35$ bicycles with probabilities of $0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}3$ and $0\mathrm{.}1,$ respectively.

a$.$ Name the decision alternatives and states of nature for this problem. $[4$ marks$]$

b$.$ Create a Payoff Table for this problem on a spreadsheet. $[11$ marks$]$

c$.$ Using a spreadsheet based on this problem, find the best action that you and your friend should opt for under each of the four decision criteria: Maximax, Maximin, Minimax Regret, and Expected Value. $[10$ marks$]$