Answer:
a) The cost function for the Wichita factory is a piecewise function, meaning it consists of different equations or formulas for different intervals or ranges of units produced.
b) Let's denote the cost per unit as C(u), where u is the number of units produced. The piecewise function for the cost per unit for production in the Wichita factory can be represented as follows:
C(u) =
$1.00, for 0 ≤ u < 1
$50.00, for 1 ≤ u < 5000
$40.00, for 5000 ≤ u < 10000
$35.00, for 10000 ≤ u < 25000
$30.00, for 25000 ≤ u ≤ 35000
c) The cost per unit for 35,000 units can be found by evaluating the cost function C(u) at u = 35,000. Based on the piecewise function mentioned above, the cost per unit for 35,000 units would be $30.00.
d) To avoid the problem of calling in workers and starting up the equipment to produce a single unit, many manufacturers implement a concept called "economies of scale." This means that they try to produce units in larger quantities to spread the fixed costs (such as labor, equipment setup, and overhead) over a greater number of units, reducing the cost per unit. By producing more units, the cost per unit decreases, making it more economically viable.
e) The best option that reflects the Cost Function for Wichita's factory is:
The plant's production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
Argument: The fact that the cost per unit decreases as the number of units produced increases indicates that the production processes are efficient and can handle longer working hours without incurring additional costs. This suggests the presence of automated processes performed by robots, which can work continuously without requiring overtime wages or incurring extra expenses.
Explanation: