A company determines that the marginal cost of producing x units of a particular commodity during a one-day operation is MC=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.
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To determine the profit-maximizing quantity of the commodity, we need to find the level of production where the marginal cost is equal to the selling price. At this point, the additional cost of producing one more unit will be equal to the revenue generated from selling that unit.
Given that the selling price is Rs.9 per unit, we can set up the equation:
MC = Selling price
16x - 1,591 = 9
To solve for x, we rearrange the equation:
16x = 9 + 1,591
16x = 1,600
x = 1,600 / 16
x = 100
Therefore, the profit-maximizing quantity of the commodity is 100 units.
To calculate the total cost, we need to consider both the fixed cost and the variable cost. The fixed cost is given as Rs.1,800 per day. The variable cost is the product of the marginal cost and the quantity produced. Thus, the total cost (TC) is:
TC = Fixed cost + (Marginal cost per unit x Quantity)
TC = 1,800 + (16x - 1,591) x 100
Now we can calculate the total cost:
TC = 1,800 + (16(100) - 1,591) x 100
TC = 1,800 + (1,600 - 1,591) x 100
TC = 1,800 + 9 x 100
TC = 1,800 + 900
TC = 2,700
Therefore, the total cost of producing 100 units of the commodity is Rs.2,700.
To calculate the profit, we need to subtract the total cost from the total revenue.
Total Revenue (TR) is given by:
TR = Selling price x Quantity
TR = 9 x 100
TR = 900
Profit (P) is calculated as:
P = TR - TC
P = 900 - 2,700
P = -1,800
Therefore, the profit from producing and selling 100 units of the commodity is -Rs.1,800. This means that the company would experience a loss of Rs.1,800 if they produce and sell 100 units.