11.1 Practice Exam

This practice exam covers material from the entire course. Work each problem on your own before comparing your result with the answer provided.

Problems

What will the future value of $5000 be in 5 years at 4% compounded quarterly?

6,100.95

A bank pays 4% compounded quarterly, what is the effective interest rate?

4.06%

Each year a sum of $2200 is placed in an IRA account paying 5%. After 10 years what will the final amount be?

27,671.36

If $5000 is invested at 4% compounded daily for 3 years, find the final amount.

5637.45

Find the present value of $200 per month at 12% for 4 years.

7,594.79

A $12,000 car loan is amortized at 6% over 6 years. Find the monthly payment.

198.87

In problem 6, what will the balance of the loan be after 4 years?

4,487.08

If in problem 6, the loan is amortized over 3 years, what will the monthly payment be?

365.06

A $42,000 car has a useful life of 6 years. It can be leased for $700 per month. If the current interest rate is 6%, is it better to lease or to buy?

buy

What monthly payment will amount to $10,000 in 5 years at 4%?

150.83

A bond has a face value of $1000 and is due in 5 years. It pays $45 interest every 6 months. If the current interest rate is 12%, what is the fair market value of the bond?

$559 . 39 + 331 . 20 = 889 . 59$

A company produces solar panels. The total cost of 20 panels is $2100, and the cost of 60 panels is $3900. Express the cost y in terms of the number of panels $x$ .

$y = 45 x + 1200$

For problems 13, 14 and 15, the final tableaux is given below

the final simplex tableau to be used for the following three problems. — **Figure 11.1**

If the initial problem is a maximization problem, what is the maximum value?

2500

If the initial problem is a maximization one, at what point does the maximum value occur?

$open parenthesis 200, 400, 100 close parenthesis$

If the initial problem is a minimization one, at what point does the minimum value occur?

$open parenthesis 75, 5, 90 close parenthesis$

At a price of $3, 100 units are demanded of a product. At a price of $5, 50 units are demanded. If $x$ is the price and $D$ the number of units demanded, write the demand equation.

$D = - 25 x + 175$

For problems 17 and 18, use the following system of equations.

$\begin{matrix} 2x & + & 4y & = & 10 \\ 3x & + & 6y & = & 15 \\ 5x & + & 10 y & = & 27 \end{matrix}$

If $x equals 1$ , what is the value of $y$ ?

No solution

How many solutions does this system have?

None

Problems 19 - 22 refer to the maximization problem below to be done using the simplex method.

A company makes two types of widgets, Regular and Deluxe. Each type of widget requires the use of three machines for its production. The Regular widget requires three hours on machine I, one hour on machine II, and one hour on machine III, and sells for $10. The Deluxe widget requires one hour on machine I, two hours on machine II, and one hour on machine III, and sells for $20. The maximum number hours available on Machines I, II, and III are 120, 100, and 40, respectively.

What are the coefficients of the objective function?

10, 20

What is the constraint imposed by Machine III?

$x sub 1 plus x sub 2 less than or equal to 40$

In solving this problem using the simplex method, how many slack variables are needed?

After the first full pivot operation, what is the current revenue?

800

A firm produces USB flash drives at a variable cost of $1.20 per drive and a fixed cost of $1800. If the drive sells for $3 each, find the break-even point.

$open parenthesis 1000, 3000 close parenthesis$

Problems 24 - 25 refer to the following minimization problem:

A diet must contain at least 60 units of protein, and 30 units of fat. Food A provides 2 grams of protein and 4 grams of fat, and costs 30 cents. Food B provides 6 grams of protein and 2 grams of fat, and costs 20 cents.

Graph the constraints, and shade the feasibility region.

Graph

Write the cost function.

$C = . 30 x + . 20 y$

For problems 26 and 27, the supply and demand equations are given as follows:

$S = 2 / 3x - 100$ , $D = - 4 / 3x + 500$ , where $x$ is the price.

Find the equilibrium price.

300

How many items will be demanded at that price?

100

If there are 5 people in a room, what is the probability that no two have the same birthday?

$.97286$

$A$ and $B$ are mutually exclusive, $P open parenthesis A close parenthesis equals .4$ , $P open parenthesis B close parenthesis equals .5$ find $P (A and B)$ .

$A$ and $B$ are independent. $P open parenthesis A close parenthesis equals .4$ , $P open parenthesis A and B close parenthesis equals .24$ , find $P (B)$ .

$.6$

What is the probability of getting 3 heads if a coin is tossed 5 times?

$.3125$

If $P open parenthesis A close parenthesis equals .5$ , $P open parenthesis B close parenthesis equals .4$ and $P open parenthesis A and B close parenthesis equals .2$ , find $P (A or B)$ .

$.7$

How many different ways can two boys and three girls be chosen from a total of 6 boys and 8 girls?

840

Problems 34 - 36 refer to the following information.

Companies $A$ , $B$ , and $C$ produce 15%, 40%, and 45% respectively of the major appliances in an area. One percent of company $A$ appliances, 2% of company $B$ appliances, and 3% of company $C$ appliances require service within the first year.

What is the probability that an appliance chosen at random is defective?

$.023$

If an appliance is chosen at random and found to be defective, what is the probability that it came from company $B$ ?

$.3478$

Suppose it was manufactured by company $B$ , what is the probability it is a defective appliance?

$.02$

On 30% of his quizzes a student receives a score of 8, and on 70% his score is 9, what is his average?

$8.7$

Problems 38 - 40 refer to the following.

An urn contains 3 red, 4 white and 5 blue marbles, and two marbles are drawn at random.

What is the chance of getting a blue marble on the second draw given that a red has been drawn on the first?

$5 / 11$

What is the probability of obtaining one white and one other marble?

$.4848$

What is the probability of obtaining at least one white marble?

$.5758$

For problems 41 - 43, consider the following transition matrix giving the probabilities for the next purchase of Tide and Brand $X$ .

Table 11.1

Next purchase

Tide

Brand

X

Present

Tide

Purchase

Brand

X

What percentage of the Tide people will buy Brand $X$ next month?

$.2$

If the original share of the market is $open parenthesis .25.75 close parenthesis$ , what will the share be two months from now?

$open bracket .6, .4 close bracket$

What will the long term share of the market be?

$open bracket 2 / 3, 1 / 3 close bracket$

For problems 44 - 46, consider the following transition matrix for an absorbing Markov Chain.

This matrix shows the probability of switching from one state to another. — **Figure 11.2**

Identify the absorbing states.

1 and 4

Write the solution matrix.

Find the probability of ending in state 4, given one started in state 2.

$.4$

Given the $3 times 3$ game $open bracket 2, 3, 3; 1, 0, minus 1; 0, 0, 4 close bracket$ , find the optimal strategy for the column player.

$open bracket 1; 0; 0 close bracket$

For problems 48 - 50, consider the following $2 times 2$ payoff matrix.

$[\begin{matrix} - 1 & 0 \\ 1 / 4 & - 1 / 4 \end{matrix}]$

Find the row player's optimal strategy.

$open bracket 1 / 3, 2 / 3 close bracket$

Find the column player's optimal strategy.

$open bracket 1 / 6; 5 / 6 close bracket$

Find the value of the game if the row and column players' strategies are $open bracket .7, .3 close bracket$ , and $open bracket .5; .5 close bracket$ , respectively.

$minus .35$

Adapted from Applied Finite Mathematics by Rupinder Sekhon (De Anza College), originally published by OpenStax CNX (cnx.org, collection col10613), licensed under CC BY 3.0. Changes were made. License: CC-BY-3.0.