A company determines that the marginal cost of producing x units of a particular commodity during a one-day operation is 16x – 1,591, where the production cost is in rupees. The selling price of a commodity is fixed at Rs.9 per unit and the fixed cost is Rs.1,800 per day. The maximum profit that can be obtained in a oneday operation is:

To find the maximum profit that can be obtained in a one-day operation, we need to determine the optimal production level that maximizes the profit.

The profit is calculated by subtracting the total cost from the total revenue. The total revenue is the selling price per unit multiplied by the number of units sold, while the total cost is the sum of the fixed cost and the marginal cost per unit multiplied by the number of units produced.

Let's break down the steps to find the maximum profit:

Step 1: Determine the optimal production level.
To find the optimal production level, we set the marginal cost equal to the selling price and solve for x:
16x - 1,591 = 9
16x = 1,591 + 9
16x = 1,600
x = 1,600 / 16
x = 100

Step 2: Calculate the total revenue.
The total revenue is the selling price per unit multiplied by the number of units sold:
Total Revenue = Selling Price * Number of Units Sold
Total Revenue = 9 * 100
Total Revenue = 900

Step 3: Calculate the total cost.
The total cost is the sum of the fixed cost and the marginal cost per unit multiplied by the number of units produced:
Total Cost = Fixed Cost + (Marginal Cost per Unit * Number of Units Produced)
Total Cost = 1,800 + (16 * 100 - 1,591)
Total Cost = 1,800 + (1,600 - 1,591)
Total Cost = 1,800 + 9
Total Cost = 1,809

Step 4: Calculate the maximum profit.
The maximum profit is obtained by subtracting the total cost from the total revenue:
Maximum Profit = Total Revenue - Total Cost
Maximum Profit = 900 - 1,809
Maximum Profit = -909

Therefore, the maximum profit that can be obtained in a one-day operation is -909 rupees. This means that the company would incur a loss of 909 rupees.