Answer:
Problem: A company with a fleet of trucks faces increasing maintenance costs as the age and mileage of the trucks increase
Identify a problem worth studying
: Yes, this problem is worth studying as it illustrate the classical optimization problem where to either minimize or maximize the outcome given some constraints. In this problem we need to maximize our profit by minimizing our maintenance cost give the age of trucks.
List the variables that affect the behavior you have identified: Lease expense, license, taxes, insurance, number of trucks, number of mechanics, type of fuel, maintenance and repair, labor, number of breakdowns, wait time to repair, loss of revenue and delay penalties, drivers retention and attrition, and number of customer reviews (negative and positive) the service.
Which variables would be neglected completely: Unless there are plans to relocate to different state with different regulations, the following variables can neglected completely: Lease expense, licenses and permits, taxes, insurance, number of trucks, number of mechanics, type of fuel.
Which might be considered as constants initially: Assuming that our mechanics are full time employees, the labor cost can be considered constant. However, the parts and materials associated with the labor are not constant. And any one time cosmetic fixes can be considered constants such as a small paint job or seat cleaning.
Can you identify any sub models you would want to study in detail?: The sub model that I want to study in more detail is as follow:
Truck ownership cost=truck depreciation+truck Return on Investment (ROI)
As the truck depreciation is constant, the main focus will be on truck Return on Investment (ROI).
Truck Return on Investment (ROI)=(the gain from the truck−Cost of investment)/cost of investment.
Hence the detailed subsystem can be as follow:
Cost of investment=(Fuel cost +maintenance cost +breakdown cost+wait cost).
Identify any data you would want collected: The data you would want collected is maintenance cost and type of maintenance and specifically the tracks and truck parts that break down the most. The wait time needed to fix and maintain the trucks. And finally customer reviews. In other words, I would collect any data that directly or indirectly impact revenues. With the collected data, I would well informed about the best time to decide replacing trucks that are performing very poorly and negatively impacting the bottom-line of the company.
Step-by-step explanation:
The specific problem is selected above and it is worth analyzing and studying because is is similar to a classical optimization problem. This is because the desired output can be either maximized or minimized by adjusting the values of certain constraints such as maintenance cost, trucks parts and other necessary parameters.
, which is a one step equation meaning that in order to solve for n you have to perform only one mathematical operation, in this case multiplication.
or 
or