PRDEAPS$/2024$

QUESTION $2$

A trade magazine is published for the manufacturing industry. Most of the large, medium and micro concerns subscribe to the magazine. The company where you are employed as an Industrial Engineer is no exception. In the last issue, the magazine produced an article where a prediction was made that the demand for motor vehicles would be high.

Apparently, South African consumer will continue buying vehicles even if car prices increases and the economy is not performing well. The magazine predicted a favourable market for motor vehicles at $70\%.$ In their opinion, the probability of an unfavourable market is $30\%.$ Senior management at your place of employment also read this article and was very sceptical of the predictions. The following table depicts the alternative and their payoffs:

$\backslash$table$[[$Model$,$Favourable market,Unfavourable market$],[$A$,$R$310000,-$R$190000],[$B$,$R$260000,-$R$90000],[$C$,$R$95000,-$R$17000]]$

Consequently, every model A would contribute R$310000$ to profit if the market is favourable and would incur a loss of R$190000$ if the market is unfavourable. The profit contribution and loss for each model are given in the table above. They requested you to prepare a report on the matter and present it at the next EXCO meeting. You are required to:

$2\mathrm{.}1$ Determine which decision model should be used.

$2\mathrm{.}2$ Compute the optimal decision.

$2\mathrm{.}3$ You believe that the R$310000$ for model A with a favourable market is too high. How much lower would this figure need to be for you to change your decision made in part $2\mathrm{.}2$ above?

$[20]$