Chapter D, Problem 16P

To determine

Net profit for the bookstore (sales-costs) over the life of $160\text{-unit}$ lot of textbooks.

Answer to Problem 16P

The correct answer is $\left(a\right)\$7900$.

Explanation of Solution

Given:

Total book lot is, $160$.

Number of semester is, $4$.

Textbook cost for producer is, $\$25$.

Bookstore is paying $\$50$ per book

Students are paying $\$75$ per book.

Students are paying $\$60$ per used book.

Bookstore repurchase $50\%$ of book at the end of each semester for $\$30$.

Calculation:

Calculate net profit for the bookstore in the beginning of first semester:

$\text{Net}\text{profit}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \\ \text{Cost}\text{for}\text{student}\end{array}\right)\\ -\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \\ \text{Cost}\text{for}\text{book}\text{store}\end{array}\right)\end{array}\right)$ ...... (I)

Substitute $160$ for Number of book sold in the first semester, $75$ for Cost for student, n > for Cost for bookstore in Equation (I).

Thus, net profit for the first semester is, $\$4,000$.

Calculate net profit for the bookstore in the beginning of second semester.

In the beginning of this semester $50\%$ of book repurchases by bookstore that sold in first semester and resold it to students.

$\text{Net}\text{profit}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \text{0}\text{.5}\\ \times \text{Cost}\text{for}\text{student}\text{for}\text{used}\text{book}\end{array}\right)\\ -\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \text{0}\text{.5}\times \\ \text{Cost}\text{for}\text{bookstore}\text{for}\text{repurchase}\end{array}\right)\end{array}\right)$ ...... (II)

Substitute $160$ for Number of book sold in the first semester, $60$ for Cost for student for used book, $30$ for Cost for bookstore for repurchase in Equation (II)

$\begin{array}{c}\text{Net}\text{profit}=\left(160\times 0.5\times 60\right)-\left(160\times 0.5\times 30\right)\\ =4,800-2,400\\ =2,400\end{array}$

Thus, net profit for the second semester is, $\$2,400$.

Calculate net profit for the bookstore in the beginning of third semester.

In the beginning of this semester $50\%$ of book repurchases by bookstore that sold in second semester and resold it to students.

$\text{Net}\text{profit=}\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \text{0}\text{.5}\times \text{0}\text{.5}\\ \times \text{Cost}\text{for}\text{student}\text{for}\text{used}\text{book}\end{array}\right)\\ -\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \\ \text{0}\text{.5}\times \text{0}\text{.5}\times \\ \text{Cost}\text{for}\text{book}\text{store}\text{for}\text{repurchase}\end{array}\right)\end{array}\right)$ ...... (III)

Substitute $160$ for Number of book sold in the first semester, $60$ for Cost for student for used book, $30$ for Cost for bookstore for repurchase in Equation (III)

$\begin{array}{c}\text{Net}\text{profit}=\left(160\times 0.5\times 0.5\times 60\right)-\left(160\times 0.5\times 0.5\times 30\right)\\ =2,400-1,200\\ =1,200\end{array}$

Thus, net profit for the third semester is $\$1,200$.

Calculate net profit for the bookstore in the third semester:

In the beginning of this semester $50\%$ of book repurchases by bookstore that sold in third semester and resold it to students. In addition, in the end of this semester bookstore repurchases $50\%$ book that sold in fourth semester.

$\text{Net}\text{profit}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \\ \text{0}\text{.5}\times \text{0}\text{.5}\times \text{0}\text{.5}\\ \text{×Cost}\text{for}\text{student}\text{for}\text{used}\text{book}\end{array}\right)\\ -\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times \text{0}\text{.5}\times \text{0}\text{.5}\times \text{0}\text{.5}\\ \times \text{Cost}\text{for}\text{book}\text{store}\text{for}\text{repurchase}\end{array}\right)\\ +\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\times \\ \text{0}\text{.5}\times \text{0}\text{.5}\times \text{0}\text{.5}\times \text{0}\text{.5}\\ \times \text{Cost}\text{for}\text{book}\text{store}\text{for}\text{repurchase}\end{array}\right)\end{array}\right)\end{array}\right)$ ...... (IV)

Substitute $160$ for Number of book sold in the first semester, $60$ for Cost for student for used book, $30$ for Cost for bookstore for repurchase in Equation (IV).

$\begin{array}{c}\text{Net}\text{profit}=\left(160\times 0.5\times 0.5\times 0.5\times 60\right)-\left(\begin{array}{l}\left(160\times 0.5\times 0.5\times 0.5\times 30\right)\\ +\left(160\times 0.5\times 0.5\times 0.5\times 0.5\times 30\right)\end{array}\right)\\ =1,200-\left(\left(600\right)+\left(300\right)\right)\\ =300\end{array}$

Thus net profit for the fourth semester is $\$300$.

Calculate total net profit.

$\text{Total}\text{net}\text{profit}=\left(\begin{array}{l}\text{Net}\text{profit}\text{for}\text{first}\text{semester}\\ \text{+Net}\text{profit}\text{for}\text{second}\text{semester}\\ \text{+Net}\text{profit}\text{for}\text{third}\text{semester}\\ \text{+Net}\text{profit}\text{for}\text{fourth}\text{semester}\end{array}\right)$ ...... (V)

Substitute $4,000$ for Net profit for first semester, $2,400$ for Net profit for second semester, $1,200$ for Net profit for the third semester, $300$ for Net profit for fourth semester in Equation (V).

$\begin{array}{c}\text{Total}\text{net}\text{profit}=4,000+2,400+1,200+300\\ =7,900\end{array}$

Thus, total cost is $\$7,900$.

Conclusion:

Therefore, the correct answer is $\left(a\right)\$7900$.