Gadgets&Co sells refrigerators. Any refrigerator that malfunctions within 3 years of purchase is replaced with a new one for free. Of all refrigerators, 3% fail during their first year of operation; 5% of the one-year-old refrigerators fail within their second year of operation, and 7% of the two-year-old refrigerators fail within their 3rd year of operation.

a) Estimate analytically the fraction of all refrigerators that will have to be replaced under the 3-year warranty scheme.

b) Construct and execute a simulation model (with 120 pseudo-realities) to estimate the fraction of all refrigerators that will have to be replaced under the 3-year warranty scheme. Explain and motivate your approach.

c) Assume that it costs $650 to replace a refrigerator, and Gadgets&Co sells 15,000 refrigerators per year. Estimate analytically the replacement cost savings per year that Gadgets&Co would achieve if they decreased their warranty period to 2 years. Explain and motivate your approach and results.

d) Use the results from part b to find a simulation-based estimate of the replacement cost savings per year that Gadgets&Co would achieve if they decreased their warranty period to 2 years. Explain and motivate your approach.