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A fast-food restaurant has a cost of production C(x) = 14x + 126 and a revenue function R(x) = 8x. When does the company start to turn a profit? Enter the exact answer. If there is no solution, enter NS. If there is an infinite number of solutions, enter IS. X = sin (a) 8 a 8

A fast-food restaurant has a cost of production C(x) = 14x + 126 and a revenue function R(x) = 8x. When does the company start to turn a profit? Enter the exact answer. If there is no solution, enter NS. If there is an infinite number of solutions, enter IS. X = sin (a) 8 a 8

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 Statement A fast-food restaurant has a cost of production \(C(x) = 14x + 126\) and a revenue function \(R(x) = 8x\). When does the company start to turn a profit? Enter the exact answer. If there is no solution, enter NS. If there is an infinite number of solutions, enter IS. ### Solution Input \[ x = \] *Here, an input box is shown where the user is expected to enter their answer.* ### Explanation To find out when the company starts to turn a profit, we need to determine the value of \(x\) where the revenue \(R(x)\) exceeds the cost \(C(x)\). We set up the equation for when the revenue equals the cost: \[ R(x) = C(x) \] \[ 8x = 14x + 126 \] Solving for \(x\) will tell us when costs and revenue are equal, which is the breakeven point. To turn a profit, we need: \[ R(x) > C(x) \] \[ 8x > 14x + 126 \] Solving this inequality will give the values of \(x\) where the company is profitable.
Transcribed Image Text:### Problem Statement A fast-food restaurant has a cost of production \(C(x) = 14x + 126\) and a revenue function \(R(x) = 8x\). When does the company start to turn a profit? Enter the exact answer. If there is no solution, enter NS. If there is an infinite number of solutions, enter IS. ### Solution Input \[ x = \] *Here, an input box is shown where the user is expected to enter their answer.* ### Explanation To find out when the company starts to turn a profit, we need to determine the value of \(x\) where the revenue \(R(x)\) exceeds the cost \(C(x)\). We set up the equation for when the revenue equals the cost: \[ R(x) = C(x) \] \[ 8x = 14x + 126 \] Solving for \(x\) will tell us when costs and revenue are equal, which is the breakeven point. To turn a profit, we need: \[ R(x) > C(x) \] \[ 8x > 14x + 126 \] Solving this inequality will give the values of \(x\) where the company is profitable.
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