a factory has fixed costs of $1,275 per month. the cost of producing each unit of its product is $2.50. each…

a factory has fixed costs of $1,275 per month. the cost of producing each unit of its product is $2.50. each unit sells for $10. the equations that model the cost and revenue for producing x units are shown. cost: c(x)=1275 + 2.5x revenue: r(x)=10x if the company sells every unit it produces, how many units must it sell in order to break even? units

a factory has fixed costs of $1,275 per month. the cost of producing each unit of its product is $2.50. each unit sells for $10. the equations that model the cost and revenue for producing x units are shown. cost: c(x)=1275 + 2.5x revenue: r(x)=10x if the company sells every unit it produces, how many units must it sell in order to break even? units

Answer

Explanation:

Step1: Set cost equal to revenue

$C(x)=R(x)$ implies $1275 + 2.5x=10x$.

Step2: Isolate x - terms

Subtract $2.5x$ from both sides: $1275=10x - 2.5x$.

Step3: Simplify right - hand side

$10x-2.5x = 7.5x$, so $1275 = 7.5x$.

Step4: Solve for x

Divide both sides by 7.5: $x=\frac{1275}{7.5}=170$.

Answer:

170