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A company produces cars that require three brakes each. They plan to produce 200,000 cars next year. They want to hold, in their ending materials inventory, enough brakes to meet 10% of next year's production requirement. They will start the year with enough brakes to manufacture 10,000 cars. How many brakes must they purchase?

Answer :

Final answer:

To determine how many brakes must be purchased, we calculate the total amount needed for production and desired ending inventory, then subtract the starting inventory. The company needs to buy 630,000 brakes for next year's production of 200,000 cars, given their inventory requirements.

Explanation:

The question asks us to calculate the number of brakes that a company needs to purchase for car production. We know that each car requires three brakes, the company plans to produce 200,000 cars next year, and they want to have an ending inventory equivalent to 10% of next year's production. They are starting with enough brakes for 10,000 cars.

Calculation of Required Brakes

To find out the total number of brakes needed, we first calculate the ending inventory required for next year:

10% of 200,000 cars = 0.10 * 200,000 = 20,000 cars.

Since each car requires three brakes,

Brakes for ending inventory = 20,000 cars * 3 brakes/car = 60,000 brakes.

Next, we calculate the total number of brakes needed for production:

200,000 cars * 3 brakes/car = 600,000 brakes.

Finally, we account for the starting inventory:

Starting inventory = 10,000 cars * 3 brakes/car = 30,000 brakes.

Brakes to purchase = Total brakes needed for production + Ending inventory brakes - Starting inventory brakes = 600,000 brakes + 60,000 brakes - 30,000 brakes = 630,000 brakes.

Therefore, the company must purchase 630,000 brakes for next year's car production.

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