Math Snap

STEP 1

Assumptions1. The cost function is $C(x)=39000+2400x$
. The revenue function is $R(x)=3150x$
3. $C(x)$ represents the total cost of producing 'x' units of a product with $39,000 as the fixed cost and$,400 as the variable cost per unit produced4. $R(x)$ represents the revenue made from selling 'x' units of the product at a price of $3,150 per unit

STEP 2

The break-even point is the point at which the cost equals the revenue. In other words, it's the point at which the company neither makes a profit nor incurs a loss. Mathematically, it can be represented as$$C(x) = R(x)$$

STEP 3

Now, plug in the given values for the cost function and the revenue function to find the break-even point.
$$39000+2400x =3150x$$

STEP 4

To solve for 'x', we need to isolate 'x' on one side of the equation. We can do this by subtracting $2400x$ from both sides of the equation.
$$39000+2400x -2400x =3150x -2400x$$

STEP 5

implify the equation.
$$39000 =750x$$

STEP 6

Now, to solve for 'x', divide both sides of the equation by750.
$$x = \frac{39000}{750}$$

Calculate the value of 'x'.
$$x = \frac{39000}{750} =52$$The break-even point is when52 units of the product are produced and sold.