Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 222 cm. A passenger wants to take a box of the maximum allowable volume. If the length and width are to be equal, what should the dimensions be?

The dimensions should be length=width=height=74 cm.

Step-by-step explanation:

We have an optimization with restriction problem.

We have to maximize the volume, subject to restriction in the sum of the length, width and height.

Let x be the length and width, that are equal, and z be the height.

The restriction can be expressed as:

We can express z in function of x as:

The volume, the function to be optimized, can be expressed as:

To optimize, we derive and equal to zero.

We have the optimum length. We can now calculate the height z:

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.