Given the cost function C(x) and the revenue function R(x), find the number of units X that must be sold to break even.
C(x) =1.2x+9000 and R(x) =1.7x
To break even, revenue must equal cost. Therefore:
1.7x = 1.2x + 9000
Simplifying:
0.5x = 9000
Dividing both sides by 0.5:
x = 18,000
Therefore, 18,000 units must be sold to break even.
An airplane takes 4 hours to travel a distance of 2200 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
To find the number of units X that must be sold to break even, we need to set the cost function C(x) equal to the revenue function R(x) and solve for X.
Setting C(x) equal to R(x), we have:
1.2x + 9000 = 1.7x
Now, let's solve for X:
1.2x - 1.7x = -9000
-0.5x = -9000
x = -9000 / -0.5
x = 18000
Therefore, 18,000 units must be sold to break even.
To find the number of units X that must be sold to break even, we need to set the cost function equal to the revenue function and solve for X.
The cost function C(x) gives the total cost of producing x units, and the revenue function R(x) gives the total revenue generated by selling x units.
So, we can set up the equation:
C(x) = R(x)
Substituting the given cost and revenue functions:
1.2x + 9000 = 1.7x
Now, let's solve for x:
1.2x - 1.7x = -9000
-0.5x = -9000
x = (-9000)/(-0.5)
x = 18,000
Therefore, 18,000 units must be sold to break even.