# Finite Mathematics - Step by step solutions of problems

Note: For detailed description of the questions, please see the attached questions file.

Below is the text that represents the brief description of the actual questions.

Question (1)

Given, f(x) = ( x + 2 )(2x - 3) , f (- 2 ) = ?

Question (2)

The equation of the line through (8 , 6 ) and (2 , - 4) is ...

Question (3)

A Revenue function is R(x) = 22x and a cost function is C(x) = - 9x + 341.

The break-even point is

(a) (17 , 374) (b) (242 , 9) (c) (11 , 242 ) (d) (31.5 , 661.5)

Question (4)

An item costs $1300 , has a scrap value of $100, and a useful life of six years.

The linear equation relating book value and number of years is

Question (5)

The solution to the system of equations

x + 3y = 12 , 4x - y = - 17 is

Question (6)

The augmented matrix ............ represents the system of equations, .........

Question (7)

The following matrix is obtained from the augmented matrix of a system of equations

............. The solution to the system is .........

Question (8)

Given the matrices A = .... and B = ....... find 3A - B

Question (9)

For the input-output matrix A, find the output required to meet the demand D

Question (10)

Select the point which is in the feasible region of the system of inequalities.

4x + y less than or equal to 8

2x + 5y less than or equal to 18 , x >= 0 , y >= 0

Question (11)

The maximum value of z = 20x + 8y subject to

3x + y <= 24

6x + 4y <= 66 , x >= 0 , y >= 0 is

Question (12)

The minimum value of z = 5x + 15y , subject to the constraints

4x + 3y>= 72 , 6x + 10y <= 174 , x >= 0 , y >= 0 occurs at

Question (13)

Find the maximum value of z = 6x + 10y in the feasible region shown in the graph below.

............

Question (14)

Pivot on the appropriate entry to find the next tableau (table given in the attachment)

Question (15)

Minimize z = 8x1 + 4x2 + 9x3 , subject to x1 + 2x2 + 5x3 >= 40

3x1 + 4x2 + x3 >= 50

2x1 + 6x2 + 7x3 >= 60

x1 >= 0 , x2 >= 0 , x3 >= 0

the initial tableau for the dual problem is

Question (16)

Set up the initial simplex tableau for the following problem.

Maximize z = 8x1 + 12x2 subject to 6x1 + 5x2 <= 30

2x1 + 3x2 >= 15

x1 + 2x2 = 6 , x1 >= 0 , x2 >= 2

Question (17)

This is a tableau from a linear programming problem (please see attachment)

The information in the tableau indicates the linear programming problem has:

(a) unique solution (b) multiple solutions (c) unbounded solutions ( d) no feasible solutions

Question (18)

The feasible region of a maximization problem shown is determined by:

12x + 5y <= 180 , 5x + 4y <= 98 , x >= 0 , y >= 0

( for the graph, please see the attachment)

Which of the following objective functions has its maximum value at (0 , 24.5) ?

(a) z = 26x + 20y (b) z = 32x + 16y (c) z = 20x + 25y (d) z = 24x + 8y

Question (19)

Find the length of a simple interest loan with P = $ 640 , r = 8.5% , and I = $ 95.20

(a) 18 months (b) 2 years (c) 11 months (d) 1.75 years

Question (20)

How much should be invested t 8% compounded semiannually in order to have $ 5000 at the end of 8 years.

Question (21)

The future value of an annuity is A = $32,000. Periodic payments are made quarterly for four years and the annuity earns 8% compounded quarterly. Find the periodic payments.

(a) $ 422.40 (b) $ 1,716.80 (c) $2,000.00 (d) $2160.00

Question (22)

{x / x is a letter of the word SEEDED } intersection { x / x is a letter of the word DRESSED } =

(a) { S , E, D} (b) {D, R, S} (c) {D, R, E, S} (d) { E }

Question (23)

If n (A) = 22, n (B) = 13, and n (A intersection B) = 6, then n(A union B) =

Question (24)

A group of people consists of 14 men and some women. One man and one woman can be selected in 252 ways. There are ____ women in the group

Question (25)

A store selects four items from a selection of 6 items to arrange in a display. How may different arrangements are possible ?

Question (26)

How many ways can three prints be selected from a collection of 10 prints ?

Question (27)

The sample space of an experiment is {A, B, C, D} and P(A) = 0.1 , P(B) = 0.3 ,

P(C) = 0.4 , P({A , C}) =

Question (28)

If the probability that at least one person makes an A on the final exam is 0.15, then the probability that no one makes an A is ?

Question (29)

For two sets E and F , n(E) = 30, n(F) = 25, and n(E intersection F) = 6. Then, P(E / F) =?

Question (30)

A student applies for two different scholarships. The probability of receiving the first scholarship is 0.3 and the probability of receiving the second is 0.4. The decisions are made independently. Find the probability the student receives exactly one scholarship

Question (31)

Estimate the population standard deviation of the grouped data

Score Frequency

1 - 3 1

4 - 6 6

7 - 9 3

Question (32)

For the following probability distribution , (meu) = ?

xi 250 300 400

pi 0.30 0.50 0.20

Question (33)

For a sample size of n = 100, proportion p = 0.6 , and at a 95% confidence level, the upper bound of the proportion is

(a) 0.096 (b) 0.696 (c) 0.050 (d) 0.025

For detailed description of the problems, with the required tables and graphs, please see the attached questions file.

#### Solution Preview

For detailed step by step solutions and working, please download the attached solution file.

Solution (1) f(-2) = 0

Solution (2)

The equation of the line through (8 , 6 ) and (2 , - 4) is 5x - 3y = 22

Solution (3)

Therefore, the break even point is (11, 242)

Solution (4)

The Book Value BV = - 200x + 1300

Solution (5)

The solution to the system of equations is (-3 , 5)

Solution (6)

The system of equations represented by the augmented matrix is .................

Solution (7)

The solution is (8 , -10 , 4)

Solution (8)

3A - B = ...

#### Solution Summary

Step by step solutions to all the above posted problems are given in the attached solution file.

The topics covered are Optimization, Linear Programming, Annuities, Compound Interest, Calculating Periodic payments, Finding system of solutions from augmented matrix, Solving given system of equations using matrix method, Sets, Finding Book Value, Problems dealing with the Salvage ( Scrap Value) and Break-Even Points, reading the values from a given graphical problem in linear programming, maximization and minimization of Objective function, writing the initial simplex tableau, and initial simplex tableau for dual problem,

problems on probability, and expected value, and many others.

Solutions are given with all the required working, formulas, graphs, and tables in such a manner that the students would be able to work out other similar problems using the given solutions as a model solutions. The solutions are presented in simplest language and using all the standard notations.