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1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X₁ + X₂ + X₃ + X₄
Subject to: X₁ + X₄%u2265 12 (shift 1)
X₁ + X₂%u2265 15 (shift 2)
X₂ + X₃%u2265 16 (shift 3)
X₃ + X₄%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above

2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)

finding the profit at every corner point of the feasible region to see which one gives the highest value.
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
locating the point that is highest on the graph.
none of the above.
all of the above.

3. Multiple optimal solutions can occur when the objective function is __________ a constraint line. (Points : 3)

unequal to
equal to
linear to
parallel to

4. When applying linear programming to diet problems, the objective function is usually designed to: (Points : 3)

maximize profits from blends of nutrients.
maximize ingredient blends.
minimize production losses.
maximize the number of products to be produced.
minimize the costs of nutrient blends.

5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 3)

same product mix, different total profit.
different product mix, same total profit as before.
same product mix, same total profit.
different product mix, different total profit.

6. The corner point solution method: (Points : 3)

will yield different results from the isoprofit line solution method.
requires that the profit from all corners of the feasible region be compared.
will provide one, and only one, optimum.
requires that all corners created by all constraints be compared.
will not provide a solution at an intersection or corner where a non-negativity constraint is involved.

7. Consider the following linear programming problem.
Maximize 4X + 10Y
Subject to: 3X + 4Y %u2264 480 and 4X + 2Y %u2264 3 360
all variables %u2265 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).

What is the maximum possible value for the objective function? (Points : 3)

1032
1200
360
none of the above

8. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is: (Points : 3)

guessing the values of the variables.
putting in a value for the objective function.
choosing the options for assuming both a linear model and non-negative variables.
resetting the parameters.
none of the above.

9. Consider the following linear programming problem.
Maximize 5X + 6Y
Subject to: 4X + 2Y %u2264 420 and 1X + 2Y %u2264 120
all variables %u2265 0

Which of the following points (X,Y) is not feasible? (Points : 3)

(50,40)
(20,50)
(60,30)
none of the above

10. ____________ is used to analyze changes in model parameters. (Points : 3)

Optimal solution
Feasible solution
Sensitivity analysis
None of the above

THIS IS A LAB REPORT THAT I NEED HELP WITH I NEED HELP WITH ANSWERING THE POST LAB QUESITON THAT IS ALL THE WAY IN THE BOTTOM PLEASE HELP ME ANSWER THE POST LAB QUESTIONS THANK YOU! THE PRE LAB I HAVE ALREADY DONE BTW!

Determination of Cobalt (II) Chloride

by UV/VIS Spectroscopy

Introduction

The absorption of specific quantities of electromagnetic (light) radiation by an element or compound allows electrons to move from lower energy level to a higher energy level. We say that the energy levels are quantized. Electrons, returning to lower energy levels, will release energy within the electromagnetic spectrum. The wavelengths may be in the ultraviolet, visible, or infra red regions of the spectrum. For cobalt (II) chloride, the compound of study, the visible region, of the spectrum will be addressed.

By knowing the wavelength (l) or frequency (n) of radiation, one may determine the energy of the transition. Relationship between energy, wavelength and frequency are:

c= ln and E= hn or E= hc/l

The light radiation absorbed in a solution of this salt is proportional to its concentration through a relationship provided by the Beer-Lambert Law:

A = kC

where A= absorbance, k is Beerâs Law constant, and C is the molar concentration in solution.

The absorbance (A), a unit-less number is dependant on the quantity of light energy absorbed and transmitted by the solution through the following equation:

A= -log T or A = 2-log %T

where T= transmittance= I/I⁰ where I is the absorbed light and I⁰ is the impinging light source.

Purpose

The purpose of this laboratory experiment is to practice, learn and carefully prepare molar solutions to investigate the relationship of concentration and spectrophotometer response. A 0.150 M solution of cobalt (II) chloride will be provided. You will prepare diluted solutions through the serial dilution method, measure the transmittance and calculate the absorbance values. You will prepare a Beerâs law graph of data; molar concentration vs. absorbance. Then determine Beerâs law constant using Microsoft Excel program.

You will also be given a concentrated sample of cobalt (II) chloride of unknown concentration and you must determine the appropriate dilution to prepare and thereafter determine the unknown concentration.

Procedure

In order to carry out this analysis procedure, it will be necessary to determine the wavelength of transition. Recall, that one specific energy maximum exists for each transition. We will study the transition in the range of 400- 600 nanometers (nm). This is the visible region of the spectrum.

Step 1. Prepare the following solution concentrations using the 0.150 M cobalt (II) chloride stock solution, 18 mm x 150 mm test tubes and Mohr pipets.

TABLE 1

Solution No.	0.150 M CoCl₂ (mL)	Volume water (mL)
1	5.0	0.0
2	4.0	1.0
3	3.5	1.5
4	3.0	2.0
5	2.5	2.5
6	2.0	3.0
7	1.0	4.0

Step 2. Carefully place a cork or rubber stopper over each solution and mix the contents.

Step 3. Measure the transmittance of a 0.150M solution between 400 nm and 600 nm at 25 nm intervals.

To accomplish this, follow these steps:

Caution: instruments are delicate. If you are uncertain about instrument operation, ask your instructor for assistance. (Instructions on instrument operation- see next page.)

SPECTRONIC is a registered trademark of Spectronic Instruments, Inc.

Instrument operation- edited version of product ^*Operatorâs Manual

Transmittance and Absorbance

1. Turn on the instrument by turning the Power Switch (10) clockwise. Allow the spectro-photometer to warm up for at least 15 minutes to stabilize.

2. After the warm-up period, set the desired wavelength with the Wavelength Control Knob.

3. Set the filter lever to the appropriate position for the selected wavelength (not required for SPECTRONICÂ® 20D).

4. Adjust the display to 0%T with the Zero Control (10). Make sure that the sample compartment is empty and the cover is closed.

5. Set the display mode to TRANSMITTANCE by pressing the MODE control key until the appropriate LED is lit.

6. Fill a clean cell with water and wipe the cell with a tissue (Kimwipe^TM) to remove liquid droplets, dust and fingerprints.

7. Place the cell in the sample compartment and align the guide mark on the cell with the guide mark at the front of the sample compartment. Press the cell firmly into the sample compartment and close the lid.

8. Carefully adjust the display to 100%T with the Transmittance/Absorbance Control (9). Move the knob slowly as you approach 100%T.

9. Remove the cell from the sample compartment and empty the water.

10. Rinse the cell twice with small volumes of the solution to be measured and fill it with the solution.

11. Wipe the cell with a tissue and insert the cell into the sample compartment. Align the guide marks and close the lid.

12. Read the appropriate value (%T) from the display.

13. Remove the cell from the sample compartment and repeat steps 10 through 12 for any remaining sample solutions.

14. When all measurements are completed, turn off the spectrophotometer by turning the Power Switch counterclockwise until it clicks.

Step 4. Using solution no. 1, follow the directions for instrument operation and record (%) transmittance values for each wavelength in Table 2.

Remember to reset the instrument to 100% for each wavelength investigated.

DO NOT DISCARD THIS SOLUTION,

Step 5. The wavelength that gives the largest absorbance value will provide the greatest sensitivity to concentration change. Generate an Excel graph of wavelength (x) vs. absorbance (y) using these values. At zero absorbance, there isnât any CoCl₂ so donât forget to include the (0,0) data point. Connect your data points with a smooth curve. This is the absorption spectrum of aqueous CoCl₂. Submit this with your lab report.

Step 6. Reset your spectrometer using this wavelength (step 5), and measure this solution and the other six solutions listed in Table 1, and record your % transmittance values in Table 3.

TABLE 2

Wavelength (nm)	% Transmittance	Absorbance
400
425
450
475
500
525
550
575
600

MAXIMUM ABSORBANCE IS LOCATED AT ________________nm.

TABLE 3 -Results measured at ______nm.

Test tube No.	% Transmittance	Absorbance	Molarity(M)
1
2
3
4
5
6
7

Step 7. Plot a graph of Molarity (M) vs. Absorbance for all seven solutions using Excel plotting techniques. This is called a calibration curve, whereby one establishes a measured response to a known solution concentration. Determine the slope of the line and include the linear equation of fit, and the correlation coefficient.

Recall the relationship A = kC or y = mx + b; where b is the (0,0) data point

Then: k = A/C

Step 8. The unknown solution to be analyzed is more concentrated than any of the standard solution concentrations that were measured to prepare the calibration curve.

Points to consider:

You must achieve a dilution such that the absorbance is within the absorbance range of the standards that were previously measured.

By using serial dilutions, will multiply many errors; thus it is best to obtain a dilution is one-step if possible.

Consider reducing the concentration by Â¾, or by Â½, and by Â¼ or to 0.10 of the original concentration and test the solution to see if the absorbance response is within range. You may also consider using the dilutions in Table 1. Once this is determined, proceed to the next step. Complete the dilution table for the diluted concentrations you prepared:

Trial	mL of unknown	mL of water	(%T)	A
1
2
3

Step 9. Using the desired dilutions, determined in step 8, measure two of the diluted solutions and record the measured transmittances in Table 4.

UNKNOWN NUMBER __________

TABLE 4

Diluted concentration (M)	Transmittance (%T)	Absorbance (A)

Calculation of absorbance, for diluted Unknown solution:

Step 10. Determine the concentration of the diluted solution using the linear equation of fit, knowing the absorbance and k, the slope of the line.

C = A/ k

Step 11: Determine the concentration in your original Unknown solution. Show your

back-calculation below to support your final answer to this experiment.

Calculations:

Unknown Solution No. ________ Concentration: ___________M

Prelab Questions

1. Consider a solution of 0.400M Co(NO₃)₂ provided by your lab instructor.

You are required to make the following dilute concentrations:

0.160M and 0.240M solutions. You are provided the following glassware: 5.0 mL Mohr pipet and 18 mm x 150 mm test tubes. Describe how you would prepare each solution, and support your description with your calculations. (Recall (M_c x V_c = M_d x V_d) where M_c is the molarity of the concentrated solution, V_c is the volume of the concentrated solution, M_d is the molarity of the dilute solution, and Vd is the volume of the diluted solution.)

Given 0.400 M Co(NO3)2 solution.

Lets say we pipette out 5 mL of this solution and dilute it to get 0.160 M solution. Then

Using, Mc x Vc = Md x Vd

0.400 x 5 = 0.160 x Vd or Vd= (0.400 x 5)/0.160 = 12.5 mL

Thus we need to add 7.5mL distilled water to 5 mL of cobalt nitrate. Since we are only provided with a 5 mL pipette, we can only measure out volumes in multiple of 5.

thus pipette out (5 x 2) 10 mL of cobalt nitrate solution in the test tube and dilute it by addition of (7.5 x2) 15 mL of distilled water.

Again for preparing 0.240 M solution

Lets say we pipette out 5 mL of this solution and dilute it to get 0.160 M solution. Then

Using, Mc x Vc = Md x Vd

0.400 x 5 = 0.240 x Vd or Vd= (0.400 x 5)/0.240 = 8.33 mL

Thus we need to add 3.33mL distilled water to 5 mL of cobalt nitrate. Again taking volumes only in multiples of 5, pipette out (5 x 3) 15 mL of cobalt nitrate solution in the test tube and dilute it by addition of (3.33 x3) 10 mL of distilled water.

2. In your own words, explain, in detail, what you will be learning during this lab. Address the chemical principles and, laboratory skills, in your answer.

Post - Lab Questions:

a) Letâs say, for a given concentration of salt solution, the maximum response at a wavelength maximum of 485nm, is 0.750. If an unknown solution is analyzed at a longer or shorter wavelength would the investigator obtain the same concentration for the Unknown solution? Explain why.

b) List all possible sources of errors that may result in this experiment.

THE ONE IN ITALICS AND BOLD IS THE PRELAB QUESTION PLEASE ANSWER THAT. PLEASE HELP ME ANSWER THE POST LAB QUESTIONS. I did THE PRE LAB. I ALSO FILLED in the tables.

Determination of Cobalt (II) Chloride

by UV/VIS Spectroscopy

Introduction

The absorption of specific quantities of electromagnetic (light) radiation by an element or compound allows electrons to move from lower energy level to a higher energy level. We say that the energy levels are quantized. Electrons, returning to lower energy levels, will release energy within the electromagnetic spectrum. The wavelengths may be in the ultraviolet, visible, or infra red regions of the spectrum. For cobalt (II) chloride, the compound of study, the visible region, of the spectrum will be addressed.

By knowing the wavelength (l) or frequency (n) of radiation, one may determine the energy of the transition. Relationship between energy, wavelength and frequency are:

c= ln and E= hn or E= hc/l

The light radiation absorbed in a solution of this salt is proportional to its concentration through a relationship provided by the Beer-Lambert Law:

A = kC

where A= absorbance, k is Beerâs Law constant, and C is the molar concentration in solution.

The absorbance (A), a unit-less number is dependant on the quantity of light energy absorbed and transmitted by the solution through the following equation:

A= -log T or A = 2-log %T

where T= transmittance= I/I⁰ where I is the absorbed light and I⁰ is the impinging light source.

Purpose

The purpose of this laboratory experiment is to practice, learn and carefully prepare molar solutions to investigate the relationship of concentration and spectrophotometer response. A 0.150 M solution of cobalt (II) chloride will be provided. You will prepare diluted solutions through the serial dilution method, measure the transmittance and calculate the absorbance values. You will prepare a Beerâs law graph of data; molar concentration vs. absorbance. Then determine Beerâs law constant using Microsoft Excel program.

You will also be given a concentrated sample of cobalt (II) chloride of unknown concentration and you must determine the appropriate dilution to prepare and thereafter determine the unknown concentration.

Procedure

In order to carry out this analysis procedure, it will be necessary to determine the wavelength of transition. Recall, that one specific energy maximum exists for each transition. We will study the transition in the range of 400- 600 nanometers (nm). This is the visible region of the spectrum.

Step 1. Prepare the following solution concentrations using the 0.150 M cobalt (II) chloride stock solution, 18 mm x 150 mm test tubes and Mohr pipets.

TABLE 1

Solution No.	0.150 M CoCl₂ (mL)	Volume water (mL)
1	5.0	0.0
2	4.0	1.0
3	3.5	1.5
4	3.0	2.0
5	2.5	2.5
6	2.0	3.0
7	1.0	4.0