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3. Decision Theory. Three radio stations call them X, Y, and Z compete for advertising share of market. At the end of last year, X has 20% of the market. Its competitors, stations Y and Z each had 40% of the market. During last year, total sales for the three stations were $100 millions and station X has a net income of 5% on its sales. Both these figures are expected to remain the same for the next year. Station X's manager suggests that if during next year X would spend additional 100 thousand dollars on selling, X would retain 85% of its customers while gaining 8% of Y's customers and 7% Z's. Company Y is expected to retain 85% of its customers while gaining 10% from X and 3% from Z. Company Z is expected to retain 90% of its customers while gaining 5%from X and 7% from Y. Should company X make the additional expenditure for selling? Justify your answer.

3. Decision Theory. Three radio stations call them X, Y, and Z compete for advertising share of market. At the end of last year, X has 20% of the market. Its competitors, stations Y and Z each had 40% of the market. During last year, total sales for the three stations were $100 millions and station X has a net income of 5% on its sales. Both these figures are expected to remain the same for the next year. Station X's manager suggests that if during next year X would spend additional 100 thousand dollars on selling, X would retain 85% of its customers while gaining 8% of Y's customers and 7% Z's. Company Y is expected to retain 85% of its customers while gaining 10% from X and 3% from Z. Company Z is expected to retain 90% of its customers while gaining 5%from X and 7% from Y. Should company X make the additional expenditure for selling? Justify your answer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section3.7: Piecewise And Step Functions
Problem 30PPS
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3. Decision Theory. Three radio stations call them X, Y, and Z compete for advertising share of market. At the end of last year, X has 20% of the market. Its competitors, stations Y and Z each had 40% of the market. During last year, total sales for the three stations were $100 millions and station X has a net income of 5% on its sales. Both these figures are expected to remain the same for the next year. Station X's manager suggests that if during next year X would spend additional 100 thousand dollars on selling, X would retain 85% of its customers while gaining 8% of Y's customers and 7% Z's. Company Y is expected to retain 85% of its customers while gaining 10% from X and 3% from Z. Company Z is expected to retain 90% of its customers while gaining 5%from X and 7% from Y. Should company X make the additional expenditure for selling? Justify your answer.
Transcribed Image Text:3. Decision Theory. Three radio stations call them X, Y, and Z compete for advertising share of market. At the end of last year, X has 20% of the market. Its competitors, stations Y and Z each had 40% of the market. During last year, total sales for the three stations were $100 millions and station X has a net income of 5% on its sales. Both these figures are expected to remain the same for the next year. Station X's manager suggests that if during next year X would spend additional 100 thousand dollars on selling, X would retain 85% of its customers while gaining 8% of Y's customers and 7% Z's. Company Y is expected to retain 85% of its customers while gaining 10% from X and 3% from Z. Company Z is expected to retain 90% of its customers while gaining 5%from X and 7% from Y. Should company X make the additional expenditure for selling? Justify your answer.
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