Question

Incubator is an enclosed apparatus whose internal environmental is isolated from ambient
environment. This is to create favorable environment hatching chicken eggs or any other bird
eggs.
All incubators have one thing in common; it regulates the temperature, humidity and provides
adequate oxygen supply in addition to turning eggs on a regular basis for 21 days.
The main functions of the incubator are:
• Egg turning: this is very important to prevent egg mortality. For egg turning, an egg
holding tray is needed. This tray is further connected to a DC gear motor which controls
its turning after every eight hours. The PLC provides the control signals to the motor
drive circuit where it provides direction and enable control signal outputs. Every 8 hours,
the PLC sets the drive signal then enables the motor drive for 30 Sec. then it resets the
direction and keeps the motor enabled for another 30 Sec. so that the egg holding tray
returns to its original position.
• Temperature: The eggs need to be kept close around 37.5 degrees Celsius at all times;
just one degree higher or lower for a few hours can terminate the embryo. The
temperature sensor provides an output of 0 Volt to 10 Volt corresponding to 0 oC to 50
oC. The PLC controls the temperature of the incubator by operating a 25 W incandescent
light bulb as a heater. It turns the light on when temperature of the incubator drops below
37.25 oC and turns it off when temperature reaches 37.75 oC.
• Humidity: 40 % to 50 % humidity must be maintained for the first 18 days; 65 to 75 percent
humidity is needed for the final days before hatching. There is a humidity sensor with an
output of 0 Volt to 10 Volt corresponding to 0 % to 100 % humidity level. The PLC controls
a vaporizer that generates water vapor to control incubator internal humidity level. For the
first 18 days, it turns the vaporizer on when humidity drops below 40%, them it turns the
vaporizer off after reaching 50% humidity level. After the 18th day, it turns the vaporizer
on when humidity drops below 65%, then it turns the vaporizer off after reaching 75%
humidity level.
• Ventilation: Eggshells are porous, allowing oxygen to enter and carbon dioxide to exit;
incubators need to have holes or vents that allow fresh air to circulate so the fetuses can
breathe. The PLC controls the operation of a ventilating fan that operates during light bulb
and vaporizer operation as well as periodically every 30 minutes for 5 minutes.

There is a buzzer and a flashing light indictor flashing at the rate of 1 Hz with a duty cycle of 50%.
The alarm is set when the humidity or temperature rises or drops below normal maintained levels
indicating incubator function failure.
The figure below shows the block diagram of the PLC controlled egg incubation system.

Use the GLOFA GM6 PLC provided with the G6F-AD2A analogue input module to supply the
required control function.
Write a ladder program with proper I/O assignment and initialization to analogue input module
to read two analogue inputs coming from the temperature and humidity sensor. The temperature
input is required to be averaged over 20 readings, while the humidity input is required to be
averaged over 30 times.
There are Start and Stop pushbuttons that controls the on/ off status of the incubator.
Provide all possible details for the Input and output modules and the GM6 PLC used in realizing
this control function.
Discussion:
Discuss the design of this egg incubator and suggest what additional elements would be required
to make this incubator capable of accepting eggs from other fowls like ducks and turkeys.

Answer 1

To solve this question just input those variables which are to be used in logistic regression, as the question talks about using two variables only that is total loans and leases to total assets & total expenses/ total assets, so we will not input total cap/assets as an input variable in our excel, here we go

As one can see, we have taken only two variables , total exp/assets and total lns & leases/ assets in calculation, follwing steps have been followed to construct the above table

1. Assume logit= b0+ b1* independent variable1+ b2* independent variable 2 , take values of b0=0.1, b1=0.1, b2=0.1, note that these values of b0, b1 and b2 are just taken for calculation, one could assume any values here for bo , b1 and b2

2. Calculate exponential of logit in the next column by using exp (value in previous column)

3. Calculate probability by using formula, probability= exp (logit)/ { 1+ exp(logit)} in the next column

4. In next column, calculate log likelihood by using formula : financial condition value (i.e. 1 or 0) * LN( probability calculated in previous column) + (1- financial condition value)* LN( 1- probability calculated in previous column)

5. take the total of the column values of log likelihood

6. use solver function in excel to change this total by putting max value of 0 and changing the variable cells containing assumed values of b0, b1 and b2 , by clicking on solve, you will get actual values of b0, b1 and b2

which comes out to be b0=-14.72, b1=89.83, b2= 8.37

therefore you will get logit as

-14.72+ 89.83* Total exp/assets+8.37*Total lns & lsses/ assets

With values given in the question as total exp/ assets= 0.11 and total loans & leases/ assets= 0.6 , we get

logit as -14.72+ 89.83* 0.11+ 8.37*0.6= 0.1833

exp (logit) = 1.20

Probability= 0.546

Loglikelihood= 1*LN(0.546)+0*LN(1-0.546)= LN(0.546)= -0.605