Omaha’s factory has yet another type of cost structure. Its cost function is provided graphically. Its maximum capacity is 38,000 units per day.


At what rate is the cost per unit decreasing for production levels above 12,000?(5 points)



State the function for the domain over [12000, 38000]. (10 points)


What is the cost per unit at the production level of 19,000? (5 points)



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.

Analysis and Making Production Decisions
You have now provided your company’s management with powerful tools that model the cost of production in the three factories. When you get an order for a certain number of units, you can be informed of the cost that would be incurred by each factory if chosen to fulfill the order. In reality, the decision must also consider many other factors, but in our scenario, we want to fill our orders at the lowest average cost per unit. Consider each of the following questions as a separate, unrelated day of business.

On Monday, you have a single request: Order A for 15,000 units. It must be fulfilled by a single factory. To which factory do you send the order? Explain your decision. Support your argument with numbers. (10 points)




On Tuesday, you have two orders. You may send each order to a separate factory OR both to the same factory. If they are both sent to be fulfilled by a single factory, you must use the total of the two orders to find that factory’s cost per unit for production on this day. Remember that the goal is to end the day with the lowest cost per unit to produce the company’s products. Order B is 7,000 units, and Order C is 30,000 units. (15 points, 5 points per part)

First, consider giving the orders to separate factories. Use these values and the following formula to calculate the average weighted cost per unit.

((cost per unit B)(#of units)+(cost per unit C)(#of units))/(Total # of units)



Second, consider sending both orders to a single factory that has the lowest cost per unit to produce 37,000 units.





Compare the two options. Decide how you will send the orders out, and document your decision by completing the daily production report below.

Production Report for Tuesday
Order # of Units Factory
B 7,000 ______
C 30,000 ______

Total # of units produced for the company today: ______
Average cost per unit for all production today: ______