Question

The production cost of an item consists of Rs. 9000
as fixed Cost, material cost Rs 12 per unit and the
labour cost as Rs x²/24 for x units produced.
find how many units should be produced to minimize
the average cost (AC)​

Answer 1

Step-by-step explanation:

Given The production cost of an item consists of Rs. 9000  as fixed Cost, material cost Rs 12 per unit and the  labour cost as Rs x²/24 for x units produced.  find how many units should be produced to minimize  the average cost (AC)

• Let the number of units produced is x
• Fixed cost will be Rs 9000
• So material cost is Rs 12 x
• Labour cost is x^2 / 24
• Therefore total cost will be 9000 + 12 x + x^2 / 24
• So dividing by x to get average cost we have
• Average cost = 9000 / x + 12 + x / 24
• Differentiating to minimize we get
• So – 9000 / x^2 + 1 / 24 = 0
• Or 9000 / x^2 = 1 / 24
• Or x^2 = 24 x 9000
• Or x = 464.75

Reference link will be

https://brainly.in/question/10569100

Answer 2

465 units should be produced to minimize  the average cost

Step-by-step explanation:

Let the number of units be 'x'

Fixed cost = Rs. 9000

Material cost = Rs. 12 per unit = Rs. 12x

Labor cost = Rs. x²/24

Production cost = Fixed cost + Material cost + Labor cost

Production cost = Rs. 9000 + Rs. 12x + Rs. x²/24

The production cost is divided by 'x' to get the average cost.

Average cost = 9000/x + 12 + x/24

Now to minimize differentiate and equate to 0,

0 = -9000/x² + 1/24

9000/x² = 1/24

x² = 9000 × 24

x² = 216000

On taking square root, we get,

∴ x = 464.75 ≈ 465 units