Question

Texts: Nazar restaurant makes a market analysis to find out that the minimum willingness to pay (WTP) for lunch is $2.5 and the maximum WTP is $12.5. Suppose that the WTP is uniformly distributed between these limits, that there are 100 lunch customers considering going to the Nazar restaurant, and that the cost of lunch is $5. a) (1 pt) The restaurant classifies anybody with WTP more than $8.5 as a high-paying customer. The rest are considered low-paying customers. The restaurant will offer à la carte service to high-paying customers and a lunch buffet for low-paying customers. Let d1, d2 denote the demand of high-paying and low-paying customers, and obtain the demand functions d1(p) and d2(p) for 2.5 ≤ p ≤ 12.5. b) (1 pt) If you are told that the demand functions are: d1(p) = min {50, 125 – 10p} d2(p) = (75-10p)+

          Texts: Nazar restaurant makes a market analysis to find out that the minimum willingness to pay (WTP) for lunch is $2.5 and the maximum WTP is $12.5. Suppose that the WTP is uniformly distributed between these limits, that there are 100 lunch customers considering going to the Nazar restaurant, and that the cost of lunch is $5.

a) (1 pt) The restaurant classifies anybody with WTP more than $8.5 as a high-paying customer. The rest are considered low-paying customers. The restaurant will offer à la carte service to high-paying customers and a lunch buffet for low-paying customers. Let d1, d2 denote the demand of high-paying and low-paying customers, and obtain the demand functions d1(p) and d2(p) for 2.5 ≤ p ≤ 12.5.

b) (1 pt) If you are told that the demand functions are: d1(p) = min {50, 125 – 10p} d2(p) = (75-10p)+

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Added by Susan R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Luke Humphrey

08/01/2023

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Step 1: To obtain the demand functions, we need to determine the number of high-paying and low-paying customers at different price levels. Show more…

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Texts: Nazar restaurant makes a market analysis to find out that the minimum willingness to pay (WTP) for lunch is $2.5 and the maximum WTP is $12.5. Suppose that the WTP is uniformly distributed between these limits, that there are 100 lunch customers considering going to the Nazar restaurant, and that the cost of lunch is $5. a) (1 pt) The restaurant classifies anybody with WTP more than $8.5 as a high-paying customer. The rest are considered low-paying customers. The restaurant will offer à la carte service to high-paying customers and a lunch buffet for low-paying customers. Let d1, d2 denote the demand of high-paying and low-paying customers, and obtain the demand functions d1(p) and d2(p) for 2.5 ≤ p ≤ 12.5. b) (1 pt) If you are told that the demand functions are: d1(p) = min {50, 125 – 10p} d2(p) = (75-10p)+

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Transcript

00:01 So in this ap statistics question, we wanna find the value of m using, and i may butcher this name, but chebyshev's inequality.

00:16 I'll call him cheb for the rest of this time.

00:23 So cheb's inequality states that for any random variable x with mean of u and a standard deviation, the probability that x deviates from its mean by more than k standard deviations is at most one over k squared.

00:44 And don't worry, we're gonna write out this formula.

00:50 So in this case, the mean of the cost of making the signature dish is 30.

01:00 The standard deviation is two.

01:04 And we wanna find the value of m such that the revenue generated from selling the dish exceeds the true cost of manufacturing it with a probability of at least 0 .99 over 100 -day period.

01:19 So let x be the random variable representing the cost of making the dish on any given day.

01:26 And the revenue generated on any day is the selling price, m, minus the cost of making the dish, x.

01:36 M equals selling price.

01:41 X equals cost of making the dish.

01:49 So we want to find m such that the revenue, m minus x, is greater than zero.

01:59 We're looking for m with a probability of at least 0 .99 for each day.

02:10 So using cheb's inequality, we can set up the following inequality.

02:16 P of m minus x greater than zero is greater than or equal to 0 .99.

02:25 So x has a mean of 30.

02:31 So we get p of x minus 30 less than m minus 30 greater than or equal to 0 .99.

02:47 Now we need to find the value of m minus 30.

02:54 And we know that cheb's inequality only provides an upper bound.

02:59 So we use the fact that the probability of x being within k standard deviations of the mean is at least one minus one over k squared...

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