What is the maximum profit that can be achieved from a vineyard business based on a specific calculation provided by the proprietor?
The maximum profit from the vineyard can be calculated by finding the point where the additional profit per bottle becomes zero. In this case, it occurs when the number of bottles produced and sold exceeds 9900. For the first 9900 bottles, the profit per bottle is $4. So, the profit from these bottles would be 9900 multiplied by $4, which equals $39,600. Beyond 9900 bottles, the profit per bottle decreases by $0.0003 for each additional bottle sold. To find the maximum profit, we need to determine the number of additional bottles that need to be sold to make the additional profit per bottle zero. The decrease in profit per bottle is given by the formula: Decrease = $0.0003 * (Number of additional bottles). Setting the decrease equal to zero, we have: $0.0003 * (Number of additional bottles) = 0. Solving for the number of additional bottles, we get: Number of additional bottles = 0 / $0.0003 = 0. Since the number of additional bottles is zero, it means that no additional bottles need to be sold beyond the initial 9900 bottles to achieve the maximum profit. Therefore, the maximum profit from the vineyard is $39,600.
Calculation for Maximum Profit in a Vineyard Business
Profit Estimation: The proprietor of a vineyard estimates that the first 9900 bottles of wine produced this season will fetch a profit of $4 per bottle. Beyond 9900 bottles, the profit per bottle decreases by $0.0003 for each additional bottle sold.
Calculation: To calculate the maximum profit, we first determine the profit from the initial 9900 bottles. This is done by multiplying the number of bottles (9900) by the profit per bottle ($4), resulting in a profit of $39,600.
Maximum Profit: The point where the additional profit per bottle becomes zero is the point of maximum profit. In this case, no additional bottles need to be sold beyond the initial 9900 bottles to achieve the maximum profit of $39,600.
Conclusion: By understanding the profit calculation and the point of maximum profit, the proprietor can optimize the vineyard business's profitability without the need to increase production beyond the initial estimate.