The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $3. The manufacturer also has fixed costs each month of $9000.
A.Find the cost function C when x energy drinks are manufactured.
C(x)=
B. Find the revenue unction R when x drinks are sold.
R(x)=
C. Find the break-even point by any method.
x= drinks.
A. The cost function C when x energy drinks are manufactured can be calculated by adding the variable cost per drink (which is $1.20) to the fixed costs per month ($9000):
C(x) = $1.20x + $9000
B. The revenue function R when x drinks are sold can be calculated by multiplying the selling price per drink (which is $3) by the number of drinks sold:
R(x) = $3x
C. The break-even point can be found by setting the cost function equal to the revenue function and solving for x:
$1.20x + $9000 = $3x
First, subtract $1.20x from both sides:
$9000 = $3x - $1.20x
Combine like terms:
$9000 = $1.80x
Divide both sides by $1.80:
x = $9000 / $1.80
x = 5000
Therefore, the break-even point is 5000 drinks.
A. The cost function C(x) can be expressed as:
C(x) = Total variable costs + Total fixed costs
The variable costs per unit are given as $1.20 per drink, so the total variable costs can be calculated as $1.20 multiplied by the number of energy drinks manufactured, x. The fixed costs are given as $9000.
Therefore, the cost function C(x) is:
C(x) = 1.20x + 9000
B. The revenue function R(x) can be expressed as:
R(x) = Price per drink x Number of drinks sold
The price per drink is given as $3, and the number of drinks sold is x.
Therefore, the revenue function R(x) is:
R(x) = 3x
C. The break-even point is the point at which the total revenue equals the total cost, meaning there is neither profit nor loss. In other words, R(x) = C(x).
To find the break-even point, we set the revenue function R(x) equal to the cost function C(x), and solve for x:
3x = 1.20x + 9000
Subtracting 1.20x from both sides:
3x - 1.20x = 9000
Simplifying:
1.80x = 9000
Dividing both sides by 1.80:
x = 9000 / 1.80
x = 5000
Therefore, the break-even point is 5000 drinks.
A. To find the cost function, you need to consider the variable costs and the fixed costs. In this case, the variable cost is $1.20 per drink, and the fixed cost is $9,000 per month.
The cost function C(x) can be calculated as follows:
C(x) = variable costs + fixed costs
As the variable cost for each drink is $1.20, the total variable cost for x drinks will be 1.20x. The fixed cost remains the same, at $9,000.
So, the cost function C(x) is:
C(x) = 1.20x + 9,000
B. To find the revenue function, you need to multiply the selling price per drink by the number of drinks sold. In this case, the selling price per drink is $3, and the number of drinks sold is x.
The revenue function R(x) can be calculated as follows:
R(x) = selling price per drink * number of drinks sold
R(x) = 3x
C. The break-even point is the point at which the revenue equals the cost, i.e., R(x) = C(x). To find the break-even point, set the revenue function R(x) equal to the cost function C(x) and solve for x.
3x = 1.20x + 9,000
2x = 9,000
x = 4,500
So, the break-even point is at x = 4,500 drinks.
The manufacturer of an energy drink spends
$
1.20
to make each drink and sells them for
$
2
. The manufacturer also has fixed costs each month of
$
10000
.
a
.
Find the cost function
C
when
x
energy drinks are manufactured.
C
(
x
)
=
b
.
Find the revenue function
R
when
x
drinks are sold.
R
(
x
)
=
c
.
Find the break-even point by any method.
x
=
drinks
C(x) = 9000 + 1.20x
R(x) = 3.00x
now just find x where C=R