Question

Two options are available to meet the annual demand of batteries in a toy company. In option 1, batteries are manufactured in the plant having fixed cost of Rupees 2,00,000 and a variable cost of Rupees 70 per unit. Option 2 consists of buying batteries from the market at a price of Rupees 90 per unit. The annual demand (in number of batteries) at which the company should switch from buying to making the batteries in the plant is .......... (Answer in integer)

Hint:

At the break-even point, compare the total costs of both options and find when they are equal. This point determines when it's more cost-effective to switch from buying to making.

Answer 1

Correct Answer: 9995

The problem involves comparing the total cost of manufacturing batteries in a plant versus purchasing them from the market. We need to find the annual demand at which these two options are equivalent to determine the point of switching from buying to manufacturing.

Let's define:
Let x be the number of batteries demanded annually.

Option 1: Manufacturing the batteries.

• Fixed Cost = ₹200,000
• Variable Cost per unit = ₹70
• Total Cost for Option 1 = Fixed Cost + (Variable Cost per unit × Number of units) = 200,000 + 70x

Option 2: Buying the batteries.

• Cost per unit = ₹90
• Total Cost for Option 2 = 90x

To find the switching point, set the total costs equal:

• 200,000 + 70x = 90x

Solving for x:

• 200,000 = 90x - 70x
• 200,000 = 20x
• x = 200,000 / 20
• x = 10,000

We must verify if this solution falls within the specified range:
The computed demand x=10,000 is greater than the given range of 9,995. Therefore, the company should switch from buying to making the batteries in the plant when the demand is 10,000 units annually.

Thus, the annual demand at which the company should switch from buying to making the batteries is 10,000.