To break even after selling 150 units, the guitar company needs the total revenue to equal the total cost. The price at which they should sell each guitar can be found by dividing the revenue function by the number of units sold, which gives us the price function P(x) = (75x + 50,000) / x.
To break even after selling 150 units, the guitar company needs the total revenue to equal the total cost. We can set up an equation with the revenue function R(x) and the cost function c(x). Since the cost of production is given by c(x) = 75x + 50,000, to break even, R(x) = 75x + 50,000. The price at which they should sell each guitar can be found by dividing the revenue function by the number of units sold, which gives us the price function P(x) = (75x + 50,000) / x. To round up to the nearest dollar, we can use the ceiling function, denoted as 'ceil', which rounds up to the nearest whole number.
The revenue function is R(x) = 75x + 50,000.