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Mathematical problem packaging
You can set a big box to hold X pieces and a small box to hold Y pieces.

According to the first scheme, three sets of equations

360/x+360/y=75

480/x+240/y=70

X= 12 y=8 can be obtained and substituted into the second scheme.

Scheme 2 600/x+ 120/y=65.

The second question, first look at the size box required for each scheme, which can be obtained by calculation.

Need a lot of boxes, need a few boxes.

Alternative 1: 30 45

Option 2: 50 15

Option 3: 40 30

Then set the packaging cost of small box as m, and the packaging cost of large box as m*( 1+k%).

Then the costs of the three schemes are as follows:

Scheme 1: 45 * m+30 * m * (1+k%) = 75 * m+30 * m * k%.

Scheme 2:15 * m+50 * m * (1+k%) = 65 * m+50 * m * k%.

Scheme 3: 30 * m+40 * m * (1+k%) = 70 * m+40 * m * k%.

Compare these three figures to see which scheme has the lowest cost.

Let the number of scheme 3 minus the number of scheme 2 =5*m- 10*m*k%.

Let the number of scheme 1 minus the number of scheme 2 = 10*m-20*m*k%.

When k is less than or equal to 25, both numbers are positive, so the cost of the second scheme is the lowest.

When k is greater than or equal to 55, both numbers are negative, so the cost of the second scheme is the highest.

In the comparison between Scheme I and Scheme III,

Scheme 1 minus Scheme 3 = 15*m- 10*m*k%.

When k is greater than or equal to 55, this number is positive, so the cost of the third scheme is the lowest.

To sum up, when k is less than or equal to 25, the cost of the second scheme is the lowest.

When k is greater than or equal to 55, the cost of scheme 3 is the lowest.