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Prob 1: Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research and development costs for products 1 and 2 are $180,000 and $160,000, respectively. Note that the first option entails no costs because research and development efforts have not yet begun. The success of these software products depends on the trend of the national economy in the coming year and on the consumers' reaction to these products. The company's revenues earned by introducing product 1 only, product 2 only, or both products in various states of the national economy are given in the following table: Decision / Trend in National Economy Strong (s1) Fair (s2) Weak (s3) Introduce neither product (d1) $0 $0 $0 Introduce product 1 only (d2) Introduce product 2 only (d3) $260,000 | $120,000 $230,000 | $100,000 $380,000 $200,000 $520,000 $420,000 Introduce both products (d4) $820,000 The probabilities of observing a strong, fair, and weak trend in the national economy in the coming year are 0.30, 0.50, and 0.20, respectively. a. Formulate a payoff table that specifies Techware's profit (in $) for each possible decision and each outcome with respect to the trend in the national economy. b. Identify the strategy that maximizes Techware's expected profit. c. Suppose that P(s1)= p, P(s2) is unchanged, find a condition of p that would change the optimal strategy in part (b).

Prob 1: Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research and development costs for products 1 and 2 are $180,000 and $160,000, respectively. Note that the first option entails no costs because research and development efforts have not yet begun. The success of these software products depends on the trend of the national economy in the coming year and on the consumers' reaction to these products. The company's revenues earned by introducing product 1 only, product 2 only, or both products in various states of the national economy are given in the following table: Decision / Trend in National Economy Strong (s1) Fair (s2) Weak (s3) Introduce neither product (d1) $0 $0 $0 Introduce product 1 only (d2) Introduce product 2 only (d3) $260,000 | $120,000 $230,000 | $100,000 $380,000 $200,000 $520,000 $420,000 Introduce both products (d4) $820,000 The probabilities of observing a strong, fair, and weak trend in the national economy in the coming year are 0.30, 0.50, and 0.20, respectively. a. Formulate a payoff table that specifies Techware's profit (in $) for each possible decision and each outcome with respect to the trend in the national economy. b. Identify the strategy that maximizes Techware's expected profit. c. Suppose that P(s1)= p, P(s2) is unchanged, find a condition of p that would change the optimal strategy in part (b).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Prob 1: Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research and development costs for products 1 and 2 are $180,000 and $160,000, respectively. Note that the first option entails no costs because research and development efforts have not yet begun. The success of these software products depends on the trend of the national economy in the coming year and on the consumers' reaction to these products. The company's revenues earned by introducing product 1 only, product 2 only, or both products in various states of the national economy are given in the following table: Decision / Trend in National Economy Strong (s1) Fair (s2) Weak (s3) Introduce neither product (d1) $0 $0 $0 Introduce product 1 only (d2) Introduce product 2 only (d3) $260,000 | $120,000 $230,000 | $100,000 $380,000 | $200,000 $520,000 $420,000 Introduce both products (d4) $820,000 The probabilities of observing a strong, fair, and weak trend in the national economy in the coming year are 0.30, 0.50, and 0.20, respectively. a. Formulate a payoff table that specifies Techware's profit (in $) for each possible decision and each outcome with respect to the trend in the national economy. b. Identify the strategy that maximizes Techware's expected profit. c. Suppose that P(s1)= p, P(s2) is unchanged, find a condition of p that would change the optimal strategy in part (b).
Transcribed Image Text:Prob 1: Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research and development costs for products 1 and 2 are $180,000 and $160,000, respectively. Note that the first option entails no costs because research and development efforts have not yet begun. The success of these software products depends on the trend of the national economy in the coming year and on the consumers' reaction to these products. The company's revenues earned by introducing product 1 only, product 2 only, or both products in various states of the national economy are given in the following table: Decision / Trend in National Economy Strong (s1) Fair (s2) Weak (s3) Introduce neither product (d1) $0 $0 $0 Introduce product 1 only (d2) Introduce product 2 only (d3) $260,000 | $120,000 $230,000 | $100,000 $380,000 | $200,000 $520,000 $420,000 Introduce both products (d4) $820,000 The probabilities of observing a strong, fair, and weak trend in the national economy in the coming year are 0.30, 0.50, and 0.20, respectively. a. Formulate a payoff table that specifies Techware's profit (in $) for each possible decision and each outcome with respect to the trend in the national economy. b. Identify the strategy that maximizes Techware's expected profit. c. Suppose that P(s1)= p, P(s2) is unchanged, find a condition of p that would change the optimal strategy in part (b).
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