Problem

Given the set of cost and revenue expressions, find the break even point and calculate the values of $q$ for which revenue exceeds cost. \[ C=2 q+14 ; \quad R=3 q \]

Solution

Step 1 :Given the cost and revenue expressions: \(C=2q+14\) and \(R=3q\).

Step 2 :The break-even point is the point at which cost equals revenue. So, we set the cost equation equal to the revenue equation and solve for \(q\): \(2q+14=3q\).

Step 3 :Solving the equation gives the break-even point as \(q = \boxed{14}\).

Step 4 :To find the values of \(q\) for which revenue exceeds cost, we solve the inequality \(R > C\) or \(3q > 2q+14\).

Step 5 :Solving the inequality gives \(q > \boxed{14}\). So, the revenue exceeds cost when \(q > 14\).

From Solvely APP
Source: https://solvelyapp.com/problems/16701/

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