Final answer:
To maximize profit, Rollins Publishing should calculate the total cost and total revenue for each textbook to find the profit, considering both the fixed and variable costs, as well as the selling price and demand. Then they must select a combination of textbooks that maximizes total profit without exceeding the total publishing capacity of 20,000 books. This may require solving a constrained optimization problem.
Step-by-step explanation:
Maximizing Profit for Rollins Publishing
To determine which textbooks Rollins Publishing should select to maximize profit, we first need to calculate the profit for each textbook. Profit is calculated by subtracting the total cost from the total revenue for each book. The total cost is the sum of the fixed cost and the total variable cost, which is the variable cost per book multiplied by the demand. The total revenue is the selling price per book multiplied by the demand.
Let's illustrate this with Book 1 as an example:
- Total Cost for Book 1 = Fixed Cost + (Variable Cost × Demand) = $12,000 + ($19 × 9,000) = $183,000
- Total Revenue for Book 1 = Selling Price × Demand = $40 × 9,000 = $360,000
- Profit for Book 1 = Total Revenue - Total Cost = $360,000 - $183,000 = $177,000
This process would be repeated for each book, but Rollins Publishing must also consider that it can only publish a total of 20,000 books. Therefore, Rollins Publishing will have to choose a combination of books that maximize total profit while not exceeding the 20,000 publishing capacity.
Once each book's profit is calculated, a constrained optimization problem can be solved, often using linear programming techniques, to select the optimal mix of textbooks to publish.