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QuestionFind the fixed cost FF and variable cost VV from the cost function C(x)C(x) using points (0, 660), (31, 1343), (95, 2750).
F=V= \begin{array}{l} F= \\ V= \end{array}

Studdy Solution

STEP 1

Assumptions1. The cost function C(x)C(x) is a linear function represented by the equation C(x)=F+VxC(x) = F + Vx, where is the fixed cost and $V$ is the variable cost per unit. . The graph of the cost function passes through the points (0,660), (31,1343), and (95,2750).
3. The point (0,660) represents the fixed cost , as this is the cost when no units are produced.
4. The variable cost VV can be found by calculating the slope of the line.

STEP 2

First, we can determine the fixed cost $$ from the y-intercept of the graph, which is the cost when no units are produced.
=C(0) = C(0)

STEP 3

Now, plug in the given value for C(0)C(0) to calculate the fixed cost $$.
=660 =660

STEP 4

Next, we need to find the variable cost VV, which is the slope of the line. The slope of a line is calculated by the change in y divided by the change in x.
V=ΔCΔxV = \frac{\Delta C}{\Delta x}

STEP 5

We can use any two points on the line to calculate the slope. Let's use the points (0,660) and (31,1343).
V=C(31)−C(0)31−0V = \frac{C(31) - C(0)}{31 -0}

STEP 6

Now, plug in the given values for C(31)C(31) and C(0)C(0) to calculate the variable cost VV.
V=1343−66031−0V = \frac{1343 -660}{31 -0}

STEP 7

Calculate the variable cost VV.
V=68331≈22.03V = \frac{683}{31} \approx22.03The fixed cost $$ is $660 and the variable cost $V$ is approximately $22.03 per unit.

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