The travel time cut down can also be the difference between making the shortage, or missing the shortage. Missing the shortage is often very expensive if you invested a lot of money in the cargo. Burn 2 to burn 4 is a 120 movespeed to 160 movespeed increase, which is 33%. Burn 4 to burn 6 is 160ms to 200ms, which is 25%.
Yeah, I covered that. Not in as much detail, but:
if you boost a fleet from burn-2 to burn-4 you've cut the travel time by 25%. If the burn level is higher than 2, you've cut the travel time by less than 25%.
Increasing movement speed by 33% is equivalent to reducing the travel time by 25%. As the base movement speed grows, the relative movement speed bonus and travel time reduction decline.
In my experience, events last long enough that if you're paying attention and not doing silly things like "ooh, let's try to cash in on that ore shortage on Agreus that we heard about two or three weeks ago," then any midrange or better burn level is generally adequate to respond before the event ends. Burn-2 is an extreme case; burn-5 or burn-6 is far more normal, and +2 burn levels do much less for you there (~18% travel time reduction; 7 days instead of 6 doesn't matter that much). There's also the little issue of the free +5 burn you receive in deep hyperspace, which screws with the efficiency of Augmented Engines quite a bit for long-distance interstellar travel.
Anyways, math:
P = gross profit per cargo unit after tariffs
D = cargo space on the ship(s) you're considering putting Augmented Engines on where Augmented Engines will affect fleet travel time
E = the rest of the cargo space available in the fleet
S = fleet daily supply consumption
X = (speed of the slower fleet)/(speed of the faster fleet)
T = time in days that the slower fleet takes to complete a journey of length L
C = per-unit supply cost
Maximum net profits ignoring fuel costs:
Slow Fleet: P*(D + E - S*T) - S*C*T
Fast Fleet: P*(0.75*D + E - S*X*T) - S*C*X*T
Setting the two equal and solving for T:
0 = P*D*(1 - 0.75) + P*E*(1 - 1) - P*S*(1 - X)*T - S*C*(1 - X)*T
0.25*P*D = S*(P + C)*(1 - X)*T
T = P*D / [4*S*(P + C)*(1 - X)]
This gives the minimum duration of a trip where the lost cargo of Augmented Engines is paid for by the savings on supply costs. A simpler, albeit less accurate, form of the equation is
which assumes that both the slow fleet and the fast fleet set aside the same amount of cargo capacity for supplies for the trip (which, despite being less accurate, may be more realistic since you probably want to have a bit of a reserve of supplies on hand).
So, what does this mean? Well, if you have a fleet consuming S = 1.5 supplies per day and you want to boost it from burn-4 to burn-6 by putting Augmented Engines on a Tarsus (D = 300, X = 0.
, and if gross profit per cargo unit after tariffs is P = 10 credits per unit with supplies costing C = 100 credits per unit, then the trip will need to last 22.7 days at burn-4 (25 days using the simplified equation) before Augmented Engines saves you enough in supplies to cover the lost potential gross profit. The longest direct route between any two stars in the base game is about 9.4 lightyears. If you somehow undertook this journey at burn-4 for the entire duration of the trip, it'd take you about 11.75 game days to complete this trip (but it won't actually, since there's a +5 burn bonus available in deep hyperspace, which you'll benefit from for some part of the journey). If you're going to make the run with a full hold one way and an empty hold the other way and if it costs nothing to add Augmented Engines to the fleet and remove them at either end of the trip, you're probably better off without Augmented Engines while the hold is full and with it while the hold is empty. If you're going to be running a full hold each way and selling all the cargo at both ends of the trip, you're definitely better off without Augmented Engines.
In my view, the case for using Augmented Engines on a trade fleet that is capable of at least moderate burn levels is very weak, unless you're underutilizing your trade fleet's capacity by enough that the lost cargo capacity doesn't matter, or unless you're at the point in the game where getting the most profit per run doesn't matter.
As far as justifying the use of Augmented Engines by its reduction in supply cost per distance traveled, I'm of the opinion that that is not sufficiently large relative to fuel costs and especially battle recovery costs to be worth worrying about, especially if you're regularly engaging in combat or interstellar travel. The trip in the example above works out to about 18 lightyears, and the fleet consumes about 27 or 34 supplies over the course of the trip. The Tarsus freighter that we know is in that fleet consumes about 36 units of fuel to complete that trip. If this is a fleet of 1 Tarsus Freighter and 2 Enforcer Destroyers, then you're looking at a fuel cost roughly 5 times that of the supply cost since fuel usually costs something close to the supply cost, and choosing Augmented Engines saves you a whole 20% on supply costs. Big deal. 5 + 0.8 is not much different from 5 + 1. It'll help a little, but not enough to make much of a difference. Battles are even worse; a single engagement which costs you only the base deployment cost of a ship typically costs you on the order of 10 or 20 days worth of supplies for the standard minimum crew of that ship.