The cost in $ of making "x" leaf blowers is given by C(x)=45x+6000.
Each blower can be sold for $60.00
a)find revenue function
b)find equation that expresees that profit for selling "x" leaf blowers.
c)How many units must be sold to break even?
To find the answers to these questions, we need to understand the concepts of revenue, profit, and the break-even point.
a) Revenue is the total amount of money generated from selling a certain quantity of products. In this case, the revenue function can be calculated by multiplying the selling price per unit with the number of units sold.
The selling price per unit is $60.00, and the number of units sold is denoted as "x." Therefore, the revenue function (R(x)) can be expressed as:
R(x) = 60x
b) Profit is the difference between the revenue earned and the cost incurred. To calculate the profit function, we subtract the cost function (C(x)) from the revenue function (R(x)).
The cost function is given as C(x) = 45x + 6000, and the revenue function is R(x) = 60x. Therefore, the profit function (P(x)) can be expressed as:
P(x) = R(x) - C(x)
= 60x - (45x + 6000)
= 60x - 45x - 6000
= 15x - 6000
c) The break-even point is the quantity at which the profit is zero, meaning that the revenue equals the cost. To find the break-even point, we set the profit function equal to zero and solve for x.
Setting P(x) = 0:
15x - 6000 = 0
Simplifying the equation:
15x = 6000
x = 6000 / 15
x = 400
Therefore, 400 units must be sold to break even.