Refer to figure.
The buffet onset boundary chart gives us the upper and lower buffet limits from high speed and high altitude flight, for a given aircraft. We enter the chart with a given load factor, mass and FL to identify the speed at which low-speed buffet will occur (the usual aerodynamic stall due to exceedance of the critical angle of attack) and the speed at which the high speed or Mach buffet occurs due to shockwave formation on the wings.

First, let's enter the chart and figure out the buffet margin with the given details:

1. We first need to calculate the load factor for a 45° bank angle. We do this using the formula n = 1/cos(φ) where n is the load factor and φ is the bank angle. In this case, we have n = 1.41 so we enter the chart from 1.4
2. Continue vertically upwards to the 110 t line, then draw a horizontal line
3. Draw two vertical lines where the horizontal line crosses FL370 (this line isn't drawn, so we need to imagine where it would be as roughly halfway between the FL360 and FL380 lines)
4. Identify the upper and lower buffet limits as M0.74 - M0.84 (the upper limit is the furthest point the curves extend to, which is M0.84)

Now reviewing the statements:

1. Flying at M = 0.80 is within the buffet free range → CORRECT

• The buffet free range is from 0.74 to 0.84, and Mach 0.80 is within the range

2. The maximum altitude that can be achieved with respect to buffet onset is higher at M = 0.76 than at M = 0.82 → INCORRECT

• By drawing vertical lines at M0.76 and M0.82, we can see where they cross our horizontal line. We can then compare the maximum altitude at each point to see which is higher
• The point where the Mach 0.82 line crosses our horizontal line is higher than FL380, whereas the point at Mach 0.76 is slightly below FL380 - which means at Mach 0.82 we can cruise slightly higher! (note that the lower lines are higher FLs)