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Mixed Worksheet for Application of Derivatives Class 12

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Case Based Passage

A company sells 1200 units of a product per year.

A company sells 1200 units of a product per year. The cost of placing one order is ₹100. The cost of holding one unit in inventory for a year is ₹ 0.50 . The company wants to find the optimal order size ( \(x\) units) to minimize its total annual inventory cost, which is the sum of ordering costs and holding costs. The average inventory level is \(x / 2\).
A company sells 1200 units of a product per year.
1. Question 1 [1 mark]
Modeling the Cost: The annual ordering cost is (Total Units / Order Size) * Cost per Order. The annual holding cost is (Average Inventory) * Holding Cost per Unit. Write the total annual inventory cost function, \(\mathrm{C}(\mathrm{x})\).
2. Question 2 [1 mark]
Finding the Rate of Change: Find the derivative of the cost function, \(C^{\prime}(x)\).
3. Question 3 [1 mark]
Minimizing Cost: Find the critical point by setting \(C^{\prime}(x)=0\). This value of \(x\) is the Economic Order Quantity (EOQ). Use the second derivative test to confirm this is a minimum.
4. Question 4 [1 mark]
Practical Application: What is the optimal number of units to order each time, and how many orders will the company place per year to minimize its costs?
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About this Mixed Worksheet

This mixed worksheet is designed for Class 12 Maths practice from Application of Derivatives Class 12. It uses the question types selected for this worksheet and keeps the preview representative of the complete set.

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