Questiona. Cost function: b. Revenue function: c. Find the break-even point by solving .
Studdy Solution
STEP 1
Assumptions1. The cost function is
. The revenue function is
3. The break-even point is the point where the cost equals the revenue
STEP 2
The cost function is already given as .
STEP 3
The revenue function is also given as .
STEP 4
To find the break-even point, we need to set the cost function equal to the revenue function and solve for . This is because at the break-even point, the cost and the revenue are equal.
STEP 5
Substitute the given cost and revenue functions into the equation.
STEP 6
To solve for , we need to get all terms involving on one side of the equation and the constants on the other side. Subtract from both sides of the equation.
STEP 7
implify the right side of the equation.
STEP 8
To isolate , divide both sides of the equation by750.
STEP 9
Calculate the value of .
STEP 10
The break-even point is when . To find the corresponding value of the cost and revenue at this point, substitute into either the cost or the revenue function.
STEP 11
Calculate the value of .
STEP 12
Therefore, the break-even point is .
The break-even point is when52 units are produced and sold, and the cost and revenue at this point are $164,800.
Was this helpful?