The average cost function for a commodity is given by AC = 0.05x^2 - 5x + 1000 + 3000/x in terms of output x. The fixed cost is Option 1: 1000 Option 2: 3000 Option 3: 5 Option 4: 0.05

Answer: 3000. Solution: The average cost function is given by AC = 0.05x^2 - 5x + 1000 + 3000/x, where x is the output. Fixed costs are costs that remain constant regardless of the number of units produced. Variable costs change with production levels. To identify the fixed cost, the Total Cost function is needed. Total Cost TC = AC x x TC = x x (0.05x^2 - 5x + 1000 + 3000/x) TC = 0.05x^3 - 5x^2 + 1000x + 3000 In the Total Cost function TC = 0.05x^3 - 5x^2 + 1000x + 3000: The terms 0.05x^3, -5x^2, and 1000x all contain x and vary with output level (variable costs). The term 3000 is independent of x and remains constant regardless of output. Therefore, the fixed cost is 3000.

Statistics & Applications

Financial Math

Medium

applied

The average cost function for a commodity is given by $AC = 0.05x^2 - 5x + 1000 + \frac{3000}{x}$ in terms of output x. The fixed cost is

1000

3000

0.05

✅ Correct Option: 2

The average cost function is given by $AC = 0.05x^2 - 5x + 1000 + \frac{3000}{x}$ , where $x$ is the output.

Fixed costs are costs that remain constant regardless of the number of units produced. Variable costs change with production levels.

To identify the fixed cost, the Total Cost function is needed.

Total Cost $TC = AC \times x$

$TC = x \times (0.05x^2 - 5x + 1000 + \frac{3000}{x})$

$TC = 0.05x^3 - 5x^2 + 1000x + 3000$

In the Total Cost function $TC = 0.05x^3 - 5x^2 + 1000x + 3000$ :

The terms $0.05x^3$ , $-5x^2$ , and $1000x$ all contain $x$ and vary with output level (variable costs).

The term $3000$ is independent of $x$ and remains constant regardless of output.

Therefore, the fixed cost is $3000$ .

2025: 2 June Shift 1

The amount of money needed to ensure for a prize of ₹ 5000 at the begining of each year indefinitely if money is worth 5% compounded annually is:

2024: 16 May Shift 1

Match List-I with List-II:

List-I Property Type	List-II EMI amount (in ₹)
(A) P	(I) 25,600
(B) Q	(II) 38,400
(C) R	(III) 32,000
(D) S	(IV) 35,200

2025: 3 June Shift 1

Match List-I with List-II

List-I	List-II
(A) Perpetuity	(I) A person deposits a fixed amount every year in his bank account to renovate his house after 10 yrs.
(B) EMI	(II) A person depositis an amount regularly in his bank account and withdraws in case of need.
(C) Sinking Fund	(III) A fixed amount is debited from the bank account of a person, every month, against a personal loan.
(D) Saving Account	(IV) A person purchased a house and rents it out.

Choose the correct answer from the options given below:

2026: 15 May Shift 1

At what rate of interest will the present value of a perpetuity of ₹1000 payable at the end of every 6 months be ₹ 20,000?

2026: 29 May Shift 1

Which of the following are correct?

(A) Sinking fund is a fixed term account.

(B) Sinking fund is set-up for a particular upcoming expense.

(D) Sinking fund can be used only for the purpose it was created.

Choose the correct answer from the options given below:

2025: 22 May Shift 2

Ajesh has set up a sinking fund in order to have ₹ 10,00,000 after 10 years for his son's education. The amount should be set aside at the end of every 6 months into an account paying 5% per annum compounded half yearly is: [given $(1.025)^{20} = 1.6386$ ]

The average cost function for a commodity is given by AC=0.05x2−5x+1000+3000xAC = 0.05x^2 - 5x + 1000 + \frac{3000}{x}AC=0.05x2−5x+1000+x3000​ in terms of output x. The fixed cost is

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The average cost function for a commodity is given by $AC = 0.05x^2 - 5x + 1000 + \frac{3000}{x}$ in terms of output x. The fixed cost is