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**Problem 17** **Given the following Total Profit function, algebraically find:** \[ \pi = -x^2 + 150x - 5000 \] 1. The profit-maximizing level of output 2. The amount of maximum profit 3. The two break-even quantities [Provide your answers on the lines provided.]

**Problem 17** **Given the following Total Profit function, algebraically find:** \[ \pi = -x^2 + 150x - 5000 \] 1. The profit-maximizing level of output 2. The amount of maximum profit 3. The two break-even quantities [Provide your answers on the lines provided.]

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 17** **Given the following Total Profit function, algebraically find:** \[ \pi = -x^2 + 150x - 5000 \] 1. The profit-maximizing level of output 2. The amount of maximum profit 3. The two break-even quantities [Provide your answers on the lines provided.]
Transcribed Image Text:**Problem 17** **Given the following Total Profit function, algebraically find:** \[ \pi = -x^2 + 150x - 5000 \] 1. The profit-maximizing level of output 2. The amount of maximum profit 3. The two break-even quantities [Provide your answers on the lines provided.]
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T=-x^2+150x-5000

T=-\left(x^2-150x\right)-5000

to do a complete square, we need to add and subtract 5625

T=-\left(x^2-150x+5625-5625\right)-5000

T=-\left(x^2-150x+75^2-5625\right)-5000

T=-\left(\left(x-75\right)^2-5625\right)-5000

T=-\left(x-75\right)^2+5625-5000

T=-\left(x-75\right)^2+625

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