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A company estimates that 1% of their products will fail after the original warranty period
but within 2 years of the purchase, with a replacement cost of $350.
If they want to offer a 2 year extended warranty, what price should they charge
so that they'll break even (in other words, so the expected profit will be 0)
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The company's cost to replace 1% of their production (which potentially will fail
after the original warranty period but within 2 years of the purchase) is
0.01*350*X dollars, where X is the rate of produced and sold units per year.
Let z be the extended insurance price in dollars per unit.
In order for the profit be zero, this equation should kept
0.01*350*X = z*X,
which gives, after canceling factor X in both sides, z = 0.01*350 = 3.5 dollars per item.
ANSWER. Under given conditions, the extended insurance price is $3.50 per item.
Solved.