Question

Assume that the situation can be expressed as a linear cost function. Find the cost function.

Fixed cost is ​$​300; 30 items cost ​$900 to produce.

Answer 1

C(q) = 20q + 300

Explanation:

Defining the cost function, when it's a linear function:

When cost can be expressed as a linear function, it's defined as the sum of the marginal cost (i.e., the slope) and the fixed cost (i.e., the y-intercept)

Cost = marginal cost + fixed cost.

In terms of variables, the linear cost equation is given by:

C(q) = mq + b, where

• C is the cost per q units made,
• m is the marginal cost (change in cost per additional items made),
• and b is the fixed cost.

Finding the cost using the information:

Since the fixed cost is $300 and 30 items cost $900, we can find m (the marginal cost) by plugging in 900 for C, 30 for q, and 300 for b:

(900 = m(30) + 300) - 300

(600 = 30m) / 30

20 = m

Thus, the marginal cost is $20.

Expressing the situation as a linear cost function:

Therefore, the situation expressed as a linear cost function is given by:

C(q) = 20q + 300