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# Academy of Management and Finance, St. Petersburg. KR-1

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**17.01.2012**

Content: spauf_1-4.zip 578,99 kB

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## Description

St. Petersburg Academy of Administration and Finance Examination 1 in mathematics. Option 4

The solution of problems of control work-1 in mathematics for students of correspondence courses, specialties: finance and credit, accounting, analysis and audit, management organizations, public municipal management. Option-4 (students whose last digit Gradebook: 4, 6, 8)

E-book (DjVu-file) contains 10 solutions control work assignments for students of the St. Petersburg Academy of Management and Finance. Solving problems presented in the form of a scanned handwriting collected into a single document of 19 pages. This document is stored in a format DjVu, which is open in Internet Explorer after installing utility program (plug-in). Link to download and install DjVu-plugin can be found on the company's homepage LIZARDTECH. DjVu-file that contains the conditions of tasks and their detailed solution completely and ready for viewing on your computer and print. All tasks were successfully offset by teachers of the St. Petersburg Academy of Management and Finance.

Topics control work tasks:

A. The algebra and geometry.

Task I. In the space of three products consider budget set at the price vector P and Q. Describe his income and his border with conventional and vector equations and inequalities, Draw budget set and its boundary graphically. In response, let the number - the amount of the budget set.

Quest II. Consider the problem of optimal scheduling matrix consumption norms A vector of specific stocks and profit from resources B.

1. Solve this problem graphically, get the optimal plan, the maximum profit, the remnants of resources. What resources are the "bottleneck" of production?

2. Make the dual problem and solve it using 2nd duality theorem and knowing the answer to the original problem of n. 1.

3. Look for the following products of vectors and matrices (do not look in the works of economic sense!) (The symbol T denotes transposition): CA, AB, ST, BC, AC ^ T, B ^ T * A, B ^ T * C * T C ^ T * B ^ T.

Quest III. Dana D depending on the demand and supply on the price of S p. Find the equilibrium price, the proceeds at the equilibrium price. Find the price at which the maximum revenue, and this very maximum revenue.

Quest IV. (Leontief model). With Dana vector non-productive consumption and the matrix A interbranch balance. Find a vector of gross output, providing the vector of consumption.

Quest V. (Neumann model). Given a matrix A, B processes, price vector P and the vector S endowments. Find intensity z1 z2 processes that maximize the value of output per production cycle, and the maximum value itself.

B. Differential calculus.

I. Setting function is set in several points of its schedule, and the schedule between adjacent points in it - the segment connecting these points. Data: (0, -2), (2, 0), (4, 3), (6, 0).

The content of the job:

1) Draw a graph of this function;

2) Describe the function by setting it on formulas intervals between adjacent points;

3) Find the domain and range of the function;

4) whether this function is increasing, monotonic, bounded, even, periodic convex?

5) Find the derivative of the function and draw the graph of the derivative;

6) Find the critical points, extrema, zeros, maximum and minimum values \u200b\u200bof the function.

Quest II. Dana parabola y = x ^ 2. Pick a new parabola with branches down to the right of this, to this parabola at the point with abscissa d = 5 smoothly (ie, without discontinuity of the derivative) is transformed into a new one. Part two parabolas form a new function. Find the derivative of the new function and draw its graph. Find the second derivative of this function and also draw its graph.

## Additional information

The document was prepared on the resource:

Online tutor in mathematics and physics.

Terms of objectives can be found at the Internet tutor section

Higher Mathematics.