The answer is ( total volume = 192 x 1/27 =192/27 =64/9) hope it helps and have a great day!
The given ratio is:

To find the unit cost per ounce, we can use proportions as follows:

Now, solve for x:

The cost per ounce (unit cost) is then $0.12/oz
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be

.
You're minimizing

subject to the constraint

. Note that

and

attain their extrema at the same values of

, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is

Take your partial derivatives and set them equal to 0:

Adding the first three equations together yields

and plugging this into the first three equations, you find a critical point at

.
The squared distance is then

, which means the shortest distance must be

.
50 miles since 1 inch equals 10 miles and there's 5 inches that means 5x10=50