DECISION TABLES $-$ CHEMSPEC Pty Ltd Chemspec Chemical produces ISOPROPYL in batches of $500$ litres, $1,000$ litres, $1,500$ litres, and $2,000$ litres. Using historical data, David Chemspec was able to determine that the probability of selling $500$ litres of ISOPROPYL is $0\mathrm{.}2.$ The probabilities of selling $1,000,1,500,$ and $2,000$ litres are $0\mathrm{.}3,0\mathrm{.}4,$ and $0\mathrm{.}1,$ respectively. he question facing David is how many litres to produce of ISOPROPYL in the next batch run. ISOPROPYL sells for R $20$ per litre. Manufacturing cost is R $12$ per litre, and handling costs and warehousing costs are estimated to be R $1$ per litre. In the past, David has allocated advertising costs to ISOPROPYL at R $3$ per litre. If ISOPROPYL is not sold after the batch run, the chemical loses much of its important properties. It can, however, be sold at a salvage value of R $13$ per litre. Furthermore, David has guaranteed to his suppliers that there will always be an adequate supply of ISOPROPYL. If David does run out, he has agreed to purchase a comparable chemical from a competitor at R$25$ per litre. David sells all of the chemical at R$20$ per litre, so his shortage means that David loses the R$5$ to buy the more expensive chemical. a$)$ Setup a suitable table and determine the profit$/$loss for each alternative in the form of a decision table. b$)$ Determine the optimum number of litres of ISOPROPYL to be produced so as to maximise profits. c$)$ Using the relevant formula, determine the expected value of perfect information