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A firm keeps a record of sales and prices over the past seven months, resulting in the following table:

$\begin{array}{lll} & \text { Price (f/ton) } & \text { Sales (tons) } \\ \text { Nov. } 1985 & 7.5 & 84.5 \\ \text { Dec. } & 8.0 & 82.0 \\ \text { Jan. } 1986 & 8.0 & 84.0 \\ \text { Feb. } & 7.2 & 92.0 \\ \text { March } & 7.0 & 95.0 \\ \text { April } & 8.0 & 92.0 \\ \text { May } & 8.5 & 91.5\end{array}$

Use these observations to estimate demand as a linear function of both price and time. Utilise this function to estimate demand for the following month, on the assumption that:
(a) price remains unchanged,
(b) price increases to $\{9 /$ ton.

Hence estimate the price elasticity of demand between these prices and find the price which would maximise sales revenue.

Given the nature of the observations, comment on any difficulties in interpreting your results for decision-making purposes.
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