Chapter D, Problem 15P

To determine

The total cost to all parties (publisher, book-store, students) over the life of the $160\text{-unit}$ lot of textbooks.

Answer to Problem 15P

The correct option is $(d)\$36,900$.

Explanation of Solution

Given:

Total book lot is $160$.

Number of semester is $4$.

Textbook cost for producer is $\$25$ per book.

Bookstore is paying $\$50$ per book.

Students are paying $\$75$ per new book.

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

At the end of each semester, the book store repurchases $50\%$ of book for $\$30$.

Calculation:

Calculate the total cost for the first semester.

$\text{Total}\text{cost}=\left(\begin{array}{l}\left(\text{Number}\text{of}\text{books}\times \text{Cost}\text{for}\text{producer}\right)\\ \text{+}\left(\text{Number}\text{of}\text{books}\times \text{Cost}\text{for}\text{bookstore}\right)\\ \text{+}\left(\text{Number}\text{of}\text{books}\times \text{Cost}\text{for}\text{student}\right)\end{array}\right)$ ...... (I)

Substitute $160$ for $\text{Number}\text{of}\text{books}$, $25$ for Cost for producer, $50$ for Cost for bookstore, $75$ for Cost for student in Equation (I).

$\begin{array}{c}\text{Total}\text{cost}=\left(160\times 25\right)+\left(160\times 50\right)+\left(160\times 75\right)\\ =4,000+8,000+12,000\\ =24,000\end{array}$

Thus, the total cost for first semester is $\$24,000$.

Calculate the total cost for second semester.

In this semester, the bookstore repurchase $50\%$ of books which was sold in the first semester.

$\text{Total}\text{cost}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times \text{Cost}\text{to}\text{bookstore for}\text{repurchase}\end{array}\right)\\ \text{+}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times \text{Cost}\text{to}\text{student}\text{for}\text{used}\text{book}\end{array}\right)\end{array}\right)$ ...... (II)

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

$\begin{array}{c}\text{Total}\text{cost}=\left(160\times 0.5\times 30\right)+\left(160\times 0.5\times 60\right)\\ =2,400+4,800\\ =7,200\end{array}$

Thus, the total cost for the second semester is $\$7,200$.

Calculate the total cost for the third semester.

In this semester, the bookstore repurchase $50\%$ book which was sold in the second semester.

$\text{Total}\text{cost}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times 0.5\times \text{Cost}\text{to}\text{bookstore}\text{for}\text{repurchare}\end{array}\right)\\ +\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times 0.5\times \text{Cost}\text{to}\text{student}\text{for}\text{used}\text{book}\end{array}\right)\end{array}\right)$ ...... (III)

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

$\begin{array}{c}\text{Total}\text{cost}=\left(160\times 0.5\times 0.5\times 30\right)+\left(160\times 0.5\times 0.5\times 60\right)\\ =1,200+2,400\\ =3,600\end{array}$

Thus, the total cost for the third semester is $\$3,600$.

Calculate the total cost for the fourth semester.

In this semester, the bookstore repurchase $50\%$ book which was sold in the third semester.

$\text{Total}\text{cost}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times 0.5\times 0.5\times \text{Cost}\text{to}\text{bookstore}\text{for}\text{repurchase}\end{array}\right)\\ \text{+}\left(\begin{array}{l}\text{Number}\text{of}\text{book}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times 0.5\times 0.5\times \text{Cost}\text{to}\text{student}\text{for}\text{used}\text{book}\end{array}\right)\end{array}\right)$ ...... (IV)

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

$\begin{array}{c}\text{Total}\text{cost}=\left(160\times 0.5\times 0.5\times 0.5\times 30\right)+\left(160\times 0.5\times 0.5\times 0.5\times 60\right)\\ =600+1,200\\ =1,800\end{array}$

Thus, the total cost for the fourth semester is $\$1800$.

Calculate the total cost at the end of the fourth semester.

At the end of the fourth semester, the bookstore repurchase $50\%$ book which was sold in fourth semester but are not sold back to the students.

$\text{Total}\text{cost=}\left(\begin{array}{l}\text{Number}\text{of}\text{books}\text{sold}\text{in}\text{first}\text{semester}\\ \times 0.5\times 0.5\times 0.5\times 0.5\times \text{Cost}\text{to}\text{bookstore}\text{for}\text{repurchase}\end{array}\right)$ ...... (V)

Substitute $160$ for Number of books sold in first semester, $30$ for Cost to bookstore for repurchase in Equation (V).

$\begin{array}{c}\text{Total}\text{cost}=\left(160\times 0.5\times 0.5\times 0.5\times 0.5\times 30\right)\\ =300\end{array}$

Thus, total cost for end of the fourth semester is $\$300$.

Now, calculate the total cost.

$\text{Total}\text{cost}=\left(\begin{array}{l}\text{Total}\text{cost}\text{for}\text{first}\text{semester}\\ +\text{Total}\text{cost}\text{for}\text{second}\text{semester}\\ +\text{Total}\text{cost}\text{for}\text{third}\text{semester}\\ +\text{Total}\text{cost}\text{for}\text{the}\text{fourth}\text{semester}\\ +\text{Total}\text{cost}\text{for}\text{the}\text{end}\text{of}\text{the}\text{semester}\end{array}\right)$ ...... (VI)

Substitute $24,000$ for Total cost for the first semester, $7,200$ for Total cost for the second semester, $3,600$ for the Total cost for the third semester, $1,800$ for Total cost for the fourth semester and $300$ for Total cost for the end of the fourth semester in Equation (VI).

$\begin{array}{c}\text{Total}\text{cost}=24,000+7,200+3,600+1,800+300\\ =36,900\end{array}$

Thus, total cost is $\$36,900$.

Conclusion:

Thus, the correct option is $(d)\$36,900$.