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प्रश्न
A certain manufacturing concern has total cost function C = 15 + 9x - 6x2 + x3. Find x, when the total cost is minimum.
उत्तर
Given C = 15 + 9x - 6x2 + x3
Differentiating with respect to 'x' we get,
`"dC"/"dx" = 9 - 12x + 3x^2`
`=> "dC"/"dx"` = 0
⇒ 9 - 12x + 3x2 = 0
⇒ x2 - 4x + 3 = 0 (Divided by 3)
⇒ (x - 1)(x - 3) = 0
⇒ x = 1, 3
Now, `("d"^2"C")/("dx"^2)` = - 12 + 6x
When x = 3,
`("d"^2"C")/("dx"^2)` = -12 + 6(3) = - 12 + 18 = 6 > 0
∴ Total cost is minimum when x = 3
∴ x = 3
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संबंधित प्रश्न
The following table gives the annual demand and unit price of 3 items.
| Items | Annual Demand (units) | Unit Price |
| A | 800 | 0.02 |
| B | 400 | 1.00 |
| C | 13,800 | 0.20 |
Ordering cost is ₹ 5 per order and holding cost is 10% of unit price. Determine the following:
- EOQ in units
- Minimum average cost
- EOQ in rupees
- EOQ in years of supply
- Number of orders per year
A dealer has to supply his customer with 400 units of a product per week. The dealer gets the product from the manufacturer at a cost of ₹ 50 per unit. The cost of ordering from the manufacturers in ₹ 75 per order. The cost of holding inventory is 7.5 % per year of the product cost. Find
- EOQ
- Total optimum cost.
