Toys Unlimited Ltd must forecast sales for a popular adult c

\"Toys Unlimited Ltd., must forecast sales for a popular adult computer game to avoid stock outs for excessive inventory charges during the upcoming Christmas season. In percentage terms, the company estimates that game sales fall at double the rate of price increases and that they grow at triple the rate of customer traffic increases. Furthermore, these effects seem to be independent.\" In the light of the statement above write an equation for estimating the Christmas season sales using the variables S=sales, P=price, T=Traffic, and t=time.

Recapping from the question above: forecast this season\'s sales if Toys Unlimited sold 10,000 games last season at $15 each, this season\'s price is anticipated to be $16.50, and customer traffic is expected to rise by 15 percent over previous levels.

Solution

As game sales fall at double the rate of price increases and that they grow at triple the rate of customer traffic increases and as they are mutually independent effects we can simple deduce the conditions and write it in equation form

S_t = S_t-1 (1 + 3* Rate of change in traffic(Change in T) - 2*Rate of change in traffic(Change in T))

     = 10000*(1+3*.15 - 2*.1) = 10000(1.25) = 12500