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Two difficult problems in mathematics.
1. Solution: For convenience, it takes X days for Team A to complete the project alone, (x+5) days for Team B, and the daily project cost of Team A is Y yuan, so the daily project cost of Team B is (y-300) yuan. Ask the number of days first, there are

1/x+1/(x+5) =1/6, arranged as x 2-7x-30 = 0, that is, (x- 10)(x+3)=0, and x >:

X= 10, x+5= 10+5= 15.

Ask each team again about the cost:

According to the meaning of the question, the daily project cost of two teams is

This gives 10200/6= 1700 (yuan).

Y+(y-300)= 1700, if it is solved, y= 1000, y-300= 1000-300=700. That is, the daily project cost of Team A is 1 1,000 yuan, and the daily project cost of Team B is 700 yuan.

At this point, Zhiyi

The total project cost for Party A to complete this project alone is10x1000 =10000 yuan.

The total project cost for Party B to complete this project alone is 15X700= 10500 yuan.

It is not difficult to see that the total project cost of Team A can save 500 yuan,

If we consider from the perspective of saving money, we should choose the A engineering team. 2. Suppose that the number of pieces of A and B are respectively

Is a and b, then a+b = 50, 9a+3b.

The profit is 700a+ 1200mb,

From the first three formulas, we can get a < =35, b < = 20,

Therefore, all possible fragments of a and b are as follows:

35, 15; 34, 16; 33, 17; 32, 18; 3 1, 19; 30,20;

To get the maximum profit, the maximum value is 700a+ 1200mb.

700 a+ 1200 b = 700 a+ 1200(50-a)= 60000-500 a,

When a takes the minimum value of 30, the maximum profit is 45000.