Suppose that you own a store that sells a particular stove for $1000. you purchase the stoves from the distributor for $800 cach. you believe that this stove has a lifetime which can be faithfully modeled as an exponential random variable with a parameter of a-1/10, where the units of time are years. you would like to offer the following extended warranty on this stove: if the stove breaks within r years, you will replace the stove completely (at a cost of $800 to you). if the stove lasts longer than r years, the extended warranty pays nothing let sc be the cost you will charge the consumer for this extended warranty. for what pairs of numbers (c, f will the expected profit you get from this warranty be zero? what do you think are reasonable choices for c and ? why?