A manufacturer sells belts for \( \$ 15 \) per unit. The fixed costs are \( \$ 1600 \) per month, and the variable cost per unit is \( \$ 11 \). (a) Write the equations of the revenue \( R(x) \) and cost \( C(x) \) functions. \( R(x)=15 x \) \( C(x)=1600+11 x \) units to break even.

To find the number of units to break even, we need to set the revenue function equal to the cost function and solve for the number of units. Given: - Revenue function: \( R(x) = 15x \) - Cost function: \( C(x) = 1600 + 11x \) To find the number of units to break even, we set the revenue function equal to the cost function: \[ R(x) = C(x) \] \[ 15x = 1600 + 11x \] Now, we can solve for \( x \) to find the number of units to break even. Solve the equation by following steps: - step0: Solve for \(x\): \(15x=1600+11x\) - step1: Move the variable to the left side: \(15x-11x=1600\) - step2: Subtract the terms: \(4x=1600\) - step3: Divide both sides: \(\frac{4x}{4}=\frac{1600}{4}\) - step4: Divide the numbers: \(x=400\) The number of units to break even is 400 units.