Company ABC manufactures a seasonal product with uncertain demand. The production cost of the product is $130 per unit, and the product will be sold to the customers at $160 per unit. The demand of the product during a selling season is normally distributed with mean 1000 and standard deviation 300. At the end of the selling season, any unsold quantity can be disposed of in a clearance sale for $80 per unit. In order to reach the required standard imposed by an ethical and sustainable supplier certification program, ABC must improve its corporate social responsibility (CSR) performance. ABC is considering two possible investments that enable it to meet the required standard. These investments will lead to a higher CSR level, which will result in greater market demand. Investment 1 has a lump-sum cost of $2000, and it will increase the mean and standard deviation of the demand by 100 units and 20 units, respectively. Investment 2 has a lump-sum cost of $3000, and it will increase the mean and standard deviation of the demand by 200 units and 40 units, respectively. (a) What will be ABC’s optimal production quantity if it undertakes Investment 1? What will be ABC’s optimal production quantity if it undertakes Investment 2? (b) Determine which of these two investments provides ABC a higher expected total profit.

Principles Of Marketing

17th Edition

ISBN:9780134492513

Author:Kotler, Philip, Armstrong, Gary (gary M.)

Publisher:Kotler, Philip, Armstrong, Gary (gary M.)

Chapter1: Marketing: Creating Customer Value And Engagement

Section: Chapter Questions

Problem 1.1DQ

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Company ABC manufactures a seasonal product with uncertain demand. The production cost of the product is $130 per unit, and the product will be sold to the customers at $160 per unit. The demand of the product during a selling season is normally distributed with mean 1000 and standard deviation 300. At the end of the selling season, any unsold quantity can be disposed of in a clearance sale for $80 per unit. In order to reach the required standard imposed by an ethical and sustainable supplier certification program, ABC must improve its corporate social responsibility (CSR) performance. ABC is considering two possible investments that enable it to meet the required standard. These investments will lead to a higher CSR level, which will result in greater market demand. Investment 1 has a lump-sum cost of $2000, and it will increase the mean and standard deviation of the demand by 100 units and 20 units, respectively. Investment 2 has a lump-sum cost of $3000, and it will increase the mean and standard deviation of the demand by 200 units and 40 units, respectively.

(a) What will be ABC’s optimal production quantity if it undertakes Investment 1? What will be ABC’s optimal production quantity if it undertakes Investment 2?

(b) Determine which of these two investments provides ABC a higher expected total profit.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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