Free FE Practice Test

# PrepFEâ„¢

## Free FE Industrial and Systems Example Practice Problems

We've selected 10 diverse practice problems from our question bank that you can use to review for the Industrial and Systems engineering FE exam and give you an idea about some of the content we provide.

## Solutions

### 1) In a manufacturing facility, widgets arrive at a rate of 20 units per hour to be processed by a single server. Processing time per widget follows an exponential distribution with a mean of 4 minutes. If the facility operates 8 hours per day, what is the average number of widgets in the system?

A.$4$
B.$8$
C.$16$
D.$\infty$

### Explanation:

Refer to the Queueing Models section in the Industrial and Systems Engineering chapter of the FE Reference Handbook.

The arrival rate is, $$\lambda = 20 \si{units/hr}$$ The service rate is, $$\mu = \frac{60 \si{min/hr}}{4 \si{min/widget}} = 15 \si{units/hr}$$ This is because there is 1 widget per 4 minutes.

Next, calculate the server utilization factor (also called the traffic intensity), $$\rho = \frac{\lambda}{(s \mu)} = \frac{20}{(1)(15)} = \frac{4}{3}$$ Now, we can calculate the average number of widgets in the system from the Single Server Models (s=1) formula, $$L = \frac{\rho}{1-\rho} = \frac{\frac{4}{3}}{1-\frac{4}{3}} = -4$$ Because $L$ is negative as a consequence of $\rho \gt 1$, this means that the system and queue will tend towards infinity over time.

### 2) You are standing next to a waste receptacle for chloroform which you happen to know is a halogenated organic. Someone goes to throw away an aluminum can in the receptacle. Your reaction is:

A.To do nothing because nothing will happen.
B.To tell them that throwing the can in the receptacle will cause an explosion.
C.To tell them that throwing the can in the receptacle will cause a release of toxic gas.
D.To tell them that throwing the can in the receptacle will cause a release of flammable gas.

### Explanation:

Refer to the Chemical Compatibility section in the Safety chapter of the FE Reference Handbook.

The problem statement tells us that chloroform is a halogenated organic. We can use the EPA Chemical Compatibility chart to find out what would happen in this scenario - that is, what are the reactivity hazards associated with halogenated organics?

The can is made of aluminum, which is an elemental metal.

Thus, if we go to the chart to the Halogenated Organics column and look down the rows until it intersects the Metal, Alkali & Alkaline Earth, Elemental row, we can see that the reactivity hazards are Heat Generation and Explosion.

Therefore, we would advise this person not to throw the aluminum can in the chloroform waste bin to avoid causing an explosion.

### 3) The very thin steel plate shown below has the following properties: Base = 20 cm Height = 10 cm Surface Density = $8.05\si{g/cm^2}$ What is most nearly the thin plate's mass moment of inertia about the centroidal x axis?

A.$53.3\si{kg-cm ^2}$
B.$28.2\si{kg-cm ^2}$
C.$8.1\si{kg-cm ^2}$
D.$13.3\si{kg-cm^2}$

### Explanation:

Refer to the Mass Moment of Inertia table in the Dynamics chapter of the FE Reference Handbook. There, you will find mass moment of inertia equations for different shapes.

Ultimately, we must solve for $$I=\frac{1}{12}Ma^2$$ Solve for the unknowns. $$M=ab\rho_s \\ M=(10\si{cm})(20\si{cm})( 8.05\si{g/cm^2}) \\ =1,610\si{g}\rightarrow 1.6\si{kg}$$ Solve for mass moment of inertia about the centroidal x axis. $$I=\frac{1}{12}(1.6\si{kg)}(10\si{cm})^2 \\ I=13.3\si{\kilo\gram \centi\meter\squared}$$ Note: This problem's x,y, and z axes are different than the x,y, and z axes used in the Mass Moment of Inertia table; therefore, $I_{xx}$ in this problem is not the same as $I_{xx}$ in the FE Reference Handbook table. Which axis is the x,y, or z is completely arbitrary. Instead, look at how the shape is oriented and its lengths to figure out which equations to use. Because our axis notation happens to be different than the axis notation used on the Mass Moment of Inertia table, the appropriate $I$ equation for this problem is not $\frac{1}{12}Mb^2$.

A.Process A
B.Process B

### Explanation:

All things being equal, according to Taguchi, a smaller variance equates to smaller costs so the better process is Process B.

### 5) What is most nearly the vector subtraction $\mathbf{B}-\mathbf{A}$ when $\mathbf{A}$=(1,2,3) and $\mathbf{B}$=(4,5,6)?

A.(3,3,3)
B.(5,7,9)
C.(-3,-3,-3)
D.(-5,-7,-9)
Refer to the Vectors section in the Mathematics chapter of the FE Reference Handbook. Subtraction of vectors can be determined by: $$\mathbf{A}-\mathbf{B}=(a_x-b_x)\mathbf{i}+(a_y-b_y)\mathbf{j}+(a_z-b_z)\mathbf{k}$$ Use the equation above to solve the vector subtraction. $$\mathbf{B}-\mathbf{A}=(4,5,6)-(1,2,3) \\ =(4-1,5-2,6-3) \\ =(3,3,3)$$