i$)$ either $0,4000$ or $8000$ kegs would be ordered;

$3$

ii$)$ if sales increased by more than $10\%,$ all extra kegs purchased would be used

during August, while if sales increased by less than this amount, only $4000$ extra

kegs would be needed.

iii$)$ if it was needed, each new keg would make only one journey in August

thereby supplying $11$ gallons of cider to customers and earning a contribution of

$$8.$

The results of his calculations are shown in the table below. This shows the

estimated changes in profit which would result for different decisions and

different levels of sales.

$($Changes in profit$)$

Sales in August $2002$

No increase on Up less than$10\%$ Up at least $10\%$

Previous year on previous year on previous year

No of

new kegs

purchased

$0$ $$0$ $$0$ $$0$

$4000-$$$16000$ $$16000$ $$16000$

$8000-$$$32000$ $$0$ $$32000$

Sally Martin, from the Marketing department, was quick to point out that these

calculations took no account of the customer goodwill which would be lost if the

Company was unable to meet demand because of a shortage of available kegs.

$"$In the long run," she said,"we could see customers asking us to remove the

pumping equipment we have installed in their bars and that could prove costly$!"$

"I still think it might be worth delaying our decision until we get the August sales

forecast," said Skills,"even if that does mean taking a risk that the kegs will not

be available."

"How reliable are these one month ahead forecasts?" asked Jewel.

"They're not bad. If you can give me a couple of days I'll let you have a summary

of their recent performance."