EX 3.21 unsold book

• Scenario Overview:

  • The bookstore purchases 10 copies of a book.
  • Cost per copy: $6.00.
  • Selling price per copy: $12.00.
  • Unsold copies can be redeemed for $2.00 each after 3 months.

• Definition of Random Variable:

  • Let $X$ represent the number of copies sold.

• Net Revenue Function:

  • The net revenue is calculated as:
  $$h(X)=12X+2(10-X)-60$$
  • Simplifying the equation:
  $$h(X)=12X+20-2X-60=10X-40$$

• Expected Values of Interest:

  • Two key expected values to consider:
    • Expected number of copies sold: $E(X)$.
    • Expected net revenue: $E(h(X))$.

• Calculation of Expected Net Revenue:

  • The expected net revenue can be expressed as:
  $$E(h(X))=E(10X-40)=10E(X)-40$$

• Implications:

  • Analyzing $E(X)$ provides insights into sales performance.
  • Calculating $E(h(X))$ helps assess overall profitability and financial outcomes for the bookstore.

• Conclusion:

  • Understanding both expected copies sold and expected net revenue is crucial for the bookstore’s financial planning and decision-making.