Emily B.
asked • 11/17/22Math Problem that i need hellp with
A company estimates that 2% 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 value will be 0)
More
1 Expert Answer
Ajay N. answered • 05/18/23
Tutor
5
(3)
Excel in Teaching Finite Math
Hi Emily,
This is a statistics and probability question.
So, the given information in the question is that the replacement cost of the products is $350.
Company estimates 2% of products are estimated to fail in a certain window (after orig. warranty period but within 2 years of purchase).
To offer a 2 year extended warranty, what price should the company charge in order to break even?
The expected value is the difference between what the company earns in revenue from selling warranty offers and the cost for replacement of failed products.
Expected Value: Revenue (from Selling warranty offers) - Cost of Replacement for failed products
Expected value is desired to be 0.
- Let x be Revenue (per warranty offer)
Expected Value: x - $350(0.02) = 0
x - 7 = 0
x = $7 (Revenue (per warranty offer)
Ajay N.
You can also do the strict 'statistics and probability' outcomes and probabilities of outcome variation of this approach for the solution: Outcomes are x (for Revenue or price to charge in the warranty offer) and -(350-x) ...which equals =350+x. So outcomes are x and [-350+x]. The probabilities of outcome are 1-0.02 = 0.98 & 0.02 respectively. So, to solve, follow the step-by-step solution approach below: x*(0.98) + (-350+x)*0.02 = 0 [Break even expected value amount] 0.98x -7+0.02x = 0 -7 + 1x = 0 1x = 7 x= $7 (should be charged per person for the 2 year extended warranty in order for the company to break even)
Report
05/18/23
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Hunter E.
P(no failure within 2 years after warranty) = 1 - 0.02 = 0.98 If a customer buys an extended warranty, the company will receive the warranty price upfront. If a product fails, the company will have to replace it at a cost of $350. If a product does not fail, the company will keep the warranty price as profit. Let's denote the warranty price as X. Then, the expected value of selling an extended warranty is: E(X) = 0.98X + 0.02(-$350) = 0.98X - $7 To break even, the expected value of selling an extended warranty should be 0, so: 0.98X - $7 = 0 0.98X = $7 X = $7 / 0.98 X = $7.14 (rounded to the nearest cent) Therefore, the company should charge at least $7.14 for a 2 year extended warranty to break even.04/16/23