A consumer is trying to decide between two long-distance callingplans. The first one charges a flat rate of $0.10 per minute, whereas the second charges a flat rate of $0.99 for calls up to 20minutes in duration and then $0.10 for each additional minuteexceeding 20 (assume that calls lasting a noninteger number ofminutes are charged proportionately to a whole-minute'scharge). Suppose the consumer's distribution of call durationis exponential with parameter λ.Which plan is better if expected call duration is 10 minutes? 15minutes? [Hint: Let h1(x) denote the cost for the firstplan when call duration is x minutes and let h2(x) bethe cost function for the second plan. Give expressions forthese two cost functions, and then determine the expected cost foreach plan.]