HOW MUCH DO TIRES COST

Question

A company manufactures tires at a cost of $40 each. The following are probabilities of defective tires in a given production run: probability of no defective tires: 10%; probability of 1% defective tires: 30%; probability of 2% defective tires: 40%; probability of 3% defective tires: 20%. When a defective tire is detected, it must be removed from the assembly line and replaced. This process adds an extra $5 to the cost of the replaced tire. What is the expected cost to the company of a batch of 3000 tires?

Answer 1

If there were no defects, the cost would be 3,000 x 40 = $120,000

there are an expected zero defective tires in 10% = 0(.1) =0

an expected 1% defective tires in 30% = (0.1)(.3) = .03 x 3000= 90

an expected 2% defective tires in 40% = .02(.4) = .08 x 3000 = 240

an expected 3% defective tires in 20% = .03(.2) = .06 x 3000 = 180

180+240+90 = 510 defective tires

510 x $5 = $2,550 cost for the expected defective tires

3000x40 = $120,000

$120,000 + $2,550 = $122,550 total expected cost for 3000 tires