Performance Task: Production Schemes
Write one or two sentences to describe the cost function for the Wichita factory.
Write the piecewise function for the cost per unit for production of units in the Wichita factory. That is, state the function , where is the number of units produced.
What is the cost per unit for 35,000 units?
According to the graph, if only one unit was produced, the cost per unit would be $1.00. In reality, the company would not call in its worker and start up the equipment to produce one unit. What safeguard do you think that many manufacturers use to avoid this type of problem?
Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the Cost Function for Wichita’s factory.
___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
___ Overtime wages were required to produce at levels above 25,000 units.
2. Factory in Seattle
Seattle’s factory is the company’s newest. It was constructed with sustainable building techniques and materials, so its cost structure has been affected in several ways. The Seattle plant uses a mix of solar power (not very reliable with so many clouds), thermal power, and wind. It has an array of batteries, so at the beginning of each production day, there is “free” stored energy that can produce up to 8,000 units. Of course, energy is just one factor of the cost of production, but it is significant.
The cost function for the Seattle factory is given by the following piecewise function. That is, is the cost function, where is the number of units produced. The plant’s maximum capacity is 42,000 units per day.
Student Guide (continued)
Production Schemes
Sketch a graph to model Seattle’s cost structure over the domain [0, 42000]. Be sure to label the axes and any endpoints where the graph breaks.
Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
At what rate is the cost per unit decreasing for production levels above 12,000?
State the function for the domain over [12000, 38000].
What is the cost per unit at the production level of 19,000?
Omaha’s city council approved a special growth incentive that decreases the company’s tax burden for production levels above last year’s average. Explain how this is reflected by the Cost Function for Omaha’s factory.
graph below
