Question

1. factory in wichita

the cost per unit for wichitas factory is graphed as a piecewise function over the domain 0, 38000

a) write one or two sentences to describe the cost function for the wichita factory.

b) write the piecewise function for the cost per unit for production of units in the wichita factory. that is, state the function c(x), where x is the number of units produced.

c) what is the cost per unit for 35,000 units?

Explanation:

Part (a)

The cost per unit for the Wichita factory is $1.00 when producing between 0 (inclusive) and 25,000 (inclusive) units, and it decreases to $0.80 per unit when producing more than 25,000 units (up to 35,000 units).

Step1: Identify intervals and corresponding costs

From the graph, we have two intervals:

• For \( 0 \leq x \leq 25000 \), the cost per unit \( C(x) = 1.0 \) (since the points \((0, 1.0)\) and \((25000, 1.0)\) are closed circles, including the endpoints).
• For \( 25000 < x \leq 35000 \), the cost per unit \( C(x) = 0.80 \) (the open circle at \( x = 25000 \) for \( y = 0.80 \) means \( x = 25000 \) is not included here, and the closed circle at \( (35000, 0.80) \) includes \( x = 35000 \)).

Step2: Write the piecewise function

Combining these intervals, the piecewise function \( C(x) \) is:

$$ C(x) =
LATEXBLOCK0
$$

Step1: Determine the interval for \( x = 35000 \)

We check the piecewise function. For \( x = 35000 \), we see that \( 25000 < 35000 \leq 35000 \), so it falls into the second interval of the piecewise function \( C(x) \).

Step2: Find the cost per unit

In the second interval (\( 25000 < x \leq 35000 \)), \( C(x) = 0.80 \). So for \( x = 35000 \), the cost per unit is \( 0.80 \) dollars.

Answer:

The cost per unit is $1.00 for production from 0 to 25,000 units (inclusive) and $0.80 for production from more than 25,000 up to 35,000 units.

Part (b)