Chapter 4.4, Problem 100E

a.

To determine

To find: the sales for Feb 2017

Answer to Problem 100E

  $26,134\text{ units}$

Explanation of Solution

Given:

The sales over the next 2 years are given by

  $S=23.1+0.442t+4.3\cos \frac{\pi t}{6}$ ….. (1)

Where S is measured in thousands of units and t is the time in months, with $t=1$ corresponding to January 2017.

Now Feb 2017 corresponds to $t=2$ .

Substitute $t=2$ , in the equation (1),

  $\begin{array}{c}S\left(2\right)=23.1+0.442\left(2\right)+4.3\cos \frac{\pi \left(2\right)}{6}\\ =26.134\end{array}$

The above sales are in thousands of units.

Conclusion:

The total sales in Feb 2017 are 26,134 units.

b.

To determine

To find: the sales for Feb 2018

Answer to Problem 100E

  $\text{31,438 units}$

Explanation of Solution

Given:

The sales over the next 2 years are given by

  $S=23.1+0.442t+4.3\cos \frac{\pi t}{6}$ ….. (1)

Where S is measured in thousands of units and t is the time in months, with $t=1$ corresponding to January 2017.

Now Feb 2018 corresponds to $t=14$ .

Substitute $t=14$ , in the equation (1),

  $\begin{array}{c}S\left(14\right)=23.1+0.442\left(14\right)+4.3\cos \frac{\pi \left(14\right)}{6}\\ =31.438\end{array}$

The above sales are in thousands of units.

Conclusion:

The total sales in Feb 2018 are 31,438 units.

c.

To determine

To find: the sales for June 2017

Answer to Problem 100E

  $21,452\text{ units}$

Explanation of Solution

Given:

The sales over the next 2 years are given by

  $S=23.1+0.442t+4.3\cos \frac{\pi t}{6}$ ….. (1)

Where S is measured in thousands of units and t is the time in months, with $t=1$ corresponding to January 2017.

Now June 2017 corresponds to $t=6$ .

Substitute $t=6$ , in the equation (1),

  $\begin{array}{c}S\left(6\right)=23.1+0.442\left(6\right)+4.3\cos \frac{\pi \left(6\right)}{6}\\ =21.452\end{array}$

The above sales are in thousands of units.

Conclusion:

The total sales in June 2017 are 21,452 units.

d.

To determine

To find: the sales for June 2018

Answer to Problem 100E

  $\text{35,356 units}$

Explanation of Solution

Given:

The sales over the next 2 years are given by

  $S=23.1+0.442t+4.3\cos \frac{\pi t}{6}$ ….. (1)

Where S is measured in thousands of units and t is the time in months, with $t=1$ corresponding to January 2017.

Now June 2018 corresponds to $t=18$ .

Substitute $t=18$ , in the equation (1),

  $\begin{array}{c}S\left(18\right)=23.1+0.442\left(18\right)+4.3\cos \frac{\pi \left(18\right)}{6}\\ =35.356\end{array}$

The above sales are in thousands of units.

Conclusion:

The total sales in June 2018 are 35,356 units.