Given the cost function C(X) =75x +106,000 and the revenue function R(x) =175x, find the number of units X that must be sold to break even
To break even, the amount of revenue generated must equal the cost incurred.
Therefore, we need to solve the equation R(x) = C(x) for x:
175x = 75x + 106,000
100x = 106,000
x = 1060
Therefore, 1060 units must be sold to break even.
To break even, the total cost (C) needs to equal the total revenue (R). Therefore, we need to find the number of units (x) that satisfies the equation C(x) = R(x).
Given:
Cost function C(x) = 75x + 106,000
Revenue function R(x) = 175x
To find the break-even point, we can set these two equations equal to each other and solve for x:
75x + 106,000 = 175x
To isolate x, we can move 75x to the right side:
106,000 = 175x - 75x
Combining like terms:
106,000 = 100x
To solve for x, divide both sides by 100:
106,000 / 100 = x
Simplifying:
1,060 = x
So, the number of units that must be sold to break even is 1,060 units.