Problems in Mathematics (Semester 2)

1. Find the determinants of matrices; .

2. Dana matrix. Find the matrix A-1 and found that AA-1 = E.

3. Solve the matrix equation:

4. Solve the system of linear equations by Cramer.

5.Firma produces two types of products: chairs and tables. To produce one chair requires 3 feet of wood for the manufacture of stola- 7 feet. On the making of a chair it takes 2 hours of working time, and for the manufacture of stola- 8 hours. Each chair brings a $ 1 profit, and every table - $ 3. How many chairs and tables should make this firm, if it has 420 feet of wood and 400 hours of working time and wants to get the maximum profit.

6.Reshit linear programming problem:
Z = 3x + 2y → max,
2x-3y≤12, -x + 2y≤6, x≤6, 2x + 5y≤20, x≥0, y≥0.

7.Reshite transport problem, sets the table:
Transportation costs to consumers.
(Mln. Rub. Per 1 thousand. Units.) Availability
(Thous. Units)
B1 B2
Warehouse A1 3 April 25
Warehouse A2 5 February 15
Query (thous. Units.) 20 20

8.Naydite solution to the problem limited to integer values \u200b\u200bof x and y.
Z = 6x + 6y → min,
3x + 2y≥12, 3x + 8y≥24, x≥2, x≥0, y≥0.

9.Naydite maximum and minimum value of the function f (x) on the interval [a, b], where:
f (x) = 2x + 1, a = 4, b = 6.
f (x) = x2-x, a = 0, b = 2.
f (x) = 3 + 2 / x, a = 1, b = 3.

I 10.Zavisimost income and expenses With the volume of production x functions defined by the following:
I (x) = - 2x2 + 20x;
C (x) = x3-35x2 + 150.
At what volume of production profits maximized if production capacity for up to 25 units?

11.Vychislit following integrals: