Lagrange multipliers:







(if

)

(if

)

(if

)
In the first octant, we assume

, so we can ignore the caveats above. Now,

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of

.
We also need to check the boundary of the region, i.e. the intersection of

with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force

, so the point we found is the only extremum.
Answer:
Two doesn’t equal 8. Theoretically, eight is the solution...
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Hence it is correct.. thanks for points.
Answer:
13 gallons
Step-by-step explanation:
42 / 3.19 = 13.166144200626959,
which can be rounded down to 13 whole gallons.