Question

QUESTION 22

A company that produces snowboards, which are seasonal products, forecasts monthly sales over the next 2 years
to be S=23.1+0.4421+4.3 cos(/6), where S is measured in thousands of units and t is the time in months, with t = 1
representing January 2010. Predict sales for following month. Round your answer to three decimal places.
June 2010
A.
S≈19.452
19,452 units
B.
S≈23.452
23,452 units
С.
S≈21452
21,452 units
D.
S≈22452
22,452 units
E.
S≈20452
20,452 units

Answer 1

A

Explanation:

To predict the sales for June 2010, we need to substitute the value of t corresponding to June 2010 into the given sales forecast equation. Since January 2010 is represented by t = 1, June 2010 would be represented by t = 6.

Plugging in t = 6 into the equation S = 23.1 + 0.4421 + 4.3 * cos(tπ/6), we get:

S = 23.1 + 0.4421 + 4.3 * cos(6π/6)

S = 23.5421 + 4.3 * cos(π)

Evaluating cos(π), we find that cos(π) = -1. Substituting this value into the equation:

S = 23.5421 + 4.3 * (-1)

S = 23.5421 - 4.3

S ≈ 19.242

Rounding the answer to three decimal places, we get S ≈ 19.242.

Therefore, the predicted sales for June 2010 (rounded to three decimal places) is approximately 19.242 thousand units.

The closest option is A. S ≈ 19.452 (19,452 units).