A company manufactures chairs at a cost of $70 each. The following are probabilities of defective chairs in a given production run: probability of 1% defective chairs: 40%; probability of 2% defective chairs: 35%; probability of 3% defective chairs: 25%. When a defective chair is detected, it must be removed from the assembly line and replaced. This process adds an extra $10 to the cost of the replaced chair. What is the expected cost to the company of a batch of 500 chairs?

Question

Mathematics

Roselyn Chen

5 April, 19:52

A company manufactures chairs at a cost of $70 each. The following are probabilities of defective chairs in a given production run: probability of 1% defective chairs: 40%; probability of 2% defective chairs: 35%; probability of 3% defective chairs: 25%. When a defective chair is detected, it must be removed from the assembly line and replaced. This process adds an extra $10 to the cost of the replaced chair. What is the expected cost to the company of a batch of 500 chairs?

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Hudson Stanton · Answer 1

C = $35,740

Step-by-step explanation:

To calculated the expected cost to the company of a batch of 500 chairs, we need to find the expected number of defective chairs on a batch of 500 chairs, it is calculated as:

D = 500 * (0.4*0.01 * + 0.35*0.02 * + 0.25*0.03)

D = 9.25 defective chairs

Because we have 500 chairs, a probability of 0.4 to have 1% defective chairs, a probability of 0.35 to have 2% defective chairs and a probability of 0.25 to have 3% defective chairs.

Now, we just need to calculated the expected cost as:

C = 500 * ($70) + 9.25 * ($70+$10)

C = $35,740

Because we have 500 chairs that cost $70 each and 9.25 defective chairs that need to be replaced with a cost of $70 plus $10.

So, the expected cost to the company of a batch of 500 chairs is equal to $35,740