Question

A company that produces snowboards which are seasonal products forecast monthly sales over the next two years to be s=2.31+0.442t+4.3cos(pit/6) where s is measured in thousands if units and t is the time in months, with t=5 representing january 2010. predict sales for the following month. round your answer to three decimal places. june 2011

Answer 1

Explanation:

To predict sales for June 2011, we need to substitute the corresponding value of t into the given sales forecast equation:

t = (month number in June 2011 - month number in January 2010) = (18 - 5) = 13

Now, let's calculate the sales (s) for June 2011:

s = 2.31 + 0.442t + 4.3 * cos(pi * t / 6)

s = 2.31 + 0.442 * 13 + 4.3 * cos(pi * 13 / 6)

s = 2.31 + 5.746 + 4.3 * cos(13pi / 6)

Note: pi is approximately equal to 3.14159.

Now, we need to calculate the cosine value:

cos(13pi / 6) ≈ cos(2.16667 * pi) ≈ cos(2 * pi - 0.975) ≈ cos(0.975) ≈ 0.549

Now, let's calculate the sales (s) for June 2011:

s ≈ 2.31 + 5.746 + 4.3 * 0.549

s ≈ 8.056 + 2.3567

s ≈ 10.412

Therefore, the predicted sales for June 2011 would be approximately 10.412 thousand units. Rounded to three decimal places, the prediction is 10.412.