Question

The total cost, TC, of producing 100 units of a good is 600 and the total cost of producing 150 units is 850. Assuming that the total cost function is linear, find an expression for TC in terms of Q, the number of units produced.

Answer 1

The linear function is given by:

$TC(q) = 5Q + 100$

The format of the linear function in this problem is:

$TC(Q) = mQ + b$

In which:

• m is the slope, which is the rate of change.
• b is the y-intercept, which is the value of y when x = 0.

We have two points (Q, TC): (100, 600) and (150, 850).

The slope is given by the change in the input divided by change in the output, thus:

$m = \frac{850 - 600}{150 - 100} = 5$

Then

$TC(q) = 5Q + b$

Point (100,600) means that when $Q = 100, TC = 600$, and this is used to find b.

$TC(q) = 5Q + b$

$600 = 5(100) + b$

$b = 100$

Thus, the function is:

$TC(q) = 5Q + 100$

A similar problem is given at https://brainly.com/question/16302622