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# 46 -During each four-hour period, the Smalltown police force…

46 -During each four-hour period, the Smalltown police force requires the following number of on-duty police officers: four from midnight to 4 a.m.; four from 4 a.m. to 8 a.m.; seven from 8 a.m. to noon; seven from noon to 4 p.m.; eight from 4 p.m. to 8 p.m.; and ten from
8 p.m. to midnight. Each police officer works two consecutive four-hour shifts.
a)Determine how to minimize the number of police of-ficers needed to meet Smalltown’s daily requirements

b)Use SolverTable to see how the number of police officers changes as the number of officers needed
from 8 a.m. to noon varies from 4 to 10.

48-NewAge Pharmaceuticals produces the drug NasaMist from four chemicals. Today, the company must pro- duce 5000 pounds of the drug. The three active ingre- dients in NasaMist are A, B, and C. By weight, at least 7% of NasaMist must consist of A, at least 5% must consist of B, and at least 3% must consist of C. The cost per pound of each chemical and the amount of each active ingredient in one pound of each chemical are given in the file P04_48.xlsx. At least 600 pounds of chemical 3 must be used.

a) Determine the cheapest way of producing today’s batch of NasaMist.

b) Use SolverTable to see how much the percentage of requirement of B is really costing NewAge. Let the percentage required vary from 3% to 8%

50-Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges
on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 220,000 pounds of grade 6 oranges and 150,000 pounds of grade 9 oranges on hand. The aver- age quality of oranges sold in bags must be at least 7, and the average quality of the oranges used to produce orange juice must be at least 8. Each pound of oranges that is used for juice yields a revenue of \$2.25 and in- curs a variable cost (consisting of labor costs, variable overhead costs, inventory costs, and so on) of \$1.35. Each pound of oranges sold in bags yields a revenue of \$2.00 and incurs a variable cost of \$1.20.

a)Determine how Sunblessed can maximize its profit.

b)Use SolverTable to determine how a change in the cost per bag of oranges changes the optimal solution.

c)Use SolverTable to determine how a change in the amount of grade 6 oranges available affects the optimal solution.

d) Use SolverTable to determine how simultaneous changes in the required average quality required for juice and the average quality required for bags change the optimal solution.

Important details and instructions about assignments:

P4-46  Worker Scheduling:  Set-up your model with the known values (INPUTs).  Use the correct color coding to illustrate whether the variable is an INPUT, OBJECTIVE/Result, or DECISION variable. When providing the “Total Employed” results, be sure to sum the “Number Starting” variables.  Include your SolverTable results (Part B).  If you are having a problem with SolverTable, view YouTube videos or contact me.

P4-48  New Age Pharmaceuticals:  For this problem it is very important to set-up your model using the correct color coding.  This will help you with your next steps – setting up the appropriate formulas to make the model operational.  With the exception of the “SUM” formula for “Lbs Used”, all other formulas are located in the “Percentage Constraints” area.  Be sure to include the constraint condition (<, <=, etc.) in your spreadsheet.  This will ensure that you set-up Solver conditions correctly.

Assuming your model is set-up correctly, SolverTable should work properly.  For percentage values, enter min .03, max .08, and increment .01.

Note: I have included the P04_48.xlsx resource spreadsheet mentioned in this problem.  You should have access to the Cengage Student Resource (where this is located); however, since it was on my PC, I thought I would send it to you.

P4-50  Sunblessed Juice Company:  Again, set-up the basic requirements in your spreadsheet model.  It is not necessary to make any changes to the structure of the template.  The key to correctly setting-up this model is make sure the “Quality Constraints” (Actual and Required) formulas are correct….and the constraint conditions are correct.  “Total Cost” and “Total Revenue” are Sumproduct functions……with “Profit” being the difference of the two values.

These are not difficult problems if you approach the set-up in logic steps and color code appropriately and include the required constraints.   Don’t forget color coding and range names.