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5) A company's sales, in millions of dollars, are modeled by the function S(1) = 0.23 – 1.82 + 4.5t + 2 {0

5) A company's sales, in millions of dollars, are modeled by the function S(1) = 0.23 – 1.82 + 4.5t + 2 {0

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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**Educational Resource: Analysis of Sales Function** **5) Company Sales Function** A company’s sales, in millions of dollars, are modeled by the function: \[ S(t) = 0.2t^3 - 1.8t^2 + 4.5t + 2 \quad \{0 \leq t \leq 5\} \] Here, \( t \) represents the number of years from today. The function is applicable only for times from 0 to 5 years inclusive. ### Questions for Analysis: **a) Identify the value(s) of \( t \), if any, where local minimums exist.** **b) Identify the value(s) of \( t \), if any, where local maximums exist.** **c) Determine the time \( t \) and the amount of sales where sales are at their highest for \( 0 \leq t \leq 5 \).** **d) Determine the time \( t \) and the amount of sales where sales are at their lowest for \( 0 \leq t \leq 5 \).** **Note:** This function can be analyzed using calculus techniques such as finding the critical points by setting the derivative \( S'(t) \) to zero. These points can help determine local minimums and maximums within the given domain.
Transcribed Image Text:**Educational Resource: Analysis of Sales Function** **5) Company Sales Function** A company’s sales, in millions of dollars, are modeled by the function: \[ S(t) = 0.2t^3 - 1.8t^2 + 4.5t + 2 \quad \{0 \leq t \leq 5\} \] Here, \( t \) represents the number of years from today. The function is applicable only for times from 0 to 5 years inclusive. ### Questions for Analysis: **a) Identify the value(s) of \( t \), if any, where local minimums exist.** **b) Identify the value(s) of \( t \), if any, where local maximums exist.** **c) Determine the time \( t \) and the amount of sales where sales are at their highest for \( 0 \leq t \leq 5 \).** **d) Determine the time \( t \) and the amount of sales where sales are at their lowest for \( 0 \leq t \leq 5 \).** **Note:** This function can be analyzed using calculus techniques such as finding the critical points by setting the derivative \( S'(t) \) to zero. These points can help determine local minimums and maximums within the given domain.
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