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

Let the annual demand be \( D \) (in number of batteries). In option 1 (making the batteries), the total cost is the sum of the fixed cost and the variable cost. 
Therefore, the total cost for option 1 is: 
\[ {Total Cost (Option 1)} = 2,00,000 + 70D \] In option 2 (buying the batteries from the market), the total cost is simply the price per battery multiplied by the number of batteries. Therefore, the total cost for option 2 is: 
\[ {Total Cost (Option 2)} = 90D \] At the break-even point, the total costs of both options are equal. Therefore, we can set the two expressions equal to each other: 
\[ 2,00,000 + 70D = 90D \] Solving for \( D \): 
\[ 2,00,000 = 90D - 70D \] \[ 2,00,000 = 20D \] \[ D = \frac{2,00,000}{20} = 10,000 \] Thus, the annual demand at which the company should switch from buying to making the batteries is approximately 10,000 batteries. Hence, the correct answer is between 9995 and 10005.