A construction company has an expenditure rate of E(x) = e 0.18X dollars per day on a particular paving job and an income rate of I(x) = 122.7 - e0.18x dollars per day on the same job, where x is the number of days from the start of the job. The company's profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. (a) Find the optimum number of days for the job to last. (b) Find the total income for the optimum number of days. (c) Find the total expenditures for the optimum number of days. (d) Find the maximum profit for the job.
A construction company has an expenditure rate of E(x) = e 0.18X dollars per day on a particular paving job and an income rate of I(x) = 122.7 - e0.18x dollars per day on the same job, where x is the number of days from the start of the job. The company's profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. (a) Find the optimum number of days for the job to last. (b) Find the total income for the optimum number of days. (c) Find the total expenditures for the optimum number of days. (d) Find the maximum profit for the job.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Transcribed Image Text:A construction company has an expenditure rate of E(x) = e0.18x dollars per day on a particular paving job and an income rate of I(x) = 122.7 - e0.18x dollars per day on
the same job, where x is the number of days from the start of the job. The company's profit on that job will equal total income less total expenditures. Profit will be
maximized if the job ends at the optimum time, which is the point where the two curves meet.
(a) Find the optimum number of days for the job to last.
(b) Find the total income for the optimum number of days.
(c) Find the total expenditures for the optimum number of days.
(d) Find the maximum profit for the job
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