A car factory produces a variable number of cars to keep up with the demand. The following measurements, made at the start of each month, show...

Question

A car factory produces a variable number of cars to keep up with the demand. The following measurements, made at the start of each month, show the rate at which cars are produced (in hundred cars/month):

Time (months)	0	1	2	3	4	5	6
Rate (hunderd cars/month)	8	12	16	19	16	15	13

A. Make an overestimate and an underestimate of the total number of cars produced in the first month. 

overestimate =   

underestimate =

B. Make an overestimate and an underestimate of the total number of cars produced for the whole six months for which we have data. 

overestimate = 

underestimate = 

Answer 1

To me, this seems like a Riemann Sum problem. Usually finding the left- and right-hand Riemann sums will give you known under- and over-estimations, based on whether the function is increasing or decreasing. Since the function we are given is both increasing and decreasing, from the points in the table, I am not completely sure if they want you to do kind of a modified version, but that's what I will propose. (The question is a little vague, I mean we could say 10 million cars for our over-estimate and 2 cars for the under-estimate based on these directions!)

My proposal: For the overestimate, use the right-hand Riemann sum for the first 3 months and then the left-hand sum for the last 3 months. Switch it around for the underestimate.

A. over = 1200 cars, under = 800 cars

B. over = 1200 + 1600 + 1900 + 1900 + 1600 + 1500 = 9700 cars

under = 800 + 1200 + 1600 + 1600 + 1500 + 1300 = 8000 cars

I could have completely misinterpreted the problem, but this is what I would do!