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Managerial Decision Making and Problem Solving. Computer Lab Notes 1. Basic Excel functions and operators. Arithmetic Operations Addition of cells A1and B1: Subtracting cell B1 from A1: Multiplication of cell A1 by B1: Division of cell A1 by B1: Cell A1xraised to the power in cell B1:. - PowerPoint PPT Presentation
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Managerial Decision Making and Problem Solving
Computer Lab Notes 1
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Basic Excel functions and operators
Arithmetic Operations– Addition of cells A1and B1:– Subtracting cell B1 from A1:– Multiplication of cell A1 by B1:– Division of cell A1 by B1:– Cell A1xraised to the power in cell B1:
= A1 + B1
= A1 - B1
= A1 * B1
= A1 / B1
= A1^ B1
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Relative and absolute addresses– All row and column references are considered relative unless
preceded by a “$” sign– When copied, ‘relative addresses’ change relative to the original
cell position.
Example: Cell E5
Cell G9
=A1+B$3+$C4+$D$6
= C5+D$3+$C8+$D$6
Basic Excel functions and operators
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Arithmetic functions– Sum =SUM(A1:A3)
Returns the sum A1+A2+A3– Average =Average(A1:A3)
Returns the arithmetic average of cells A1, A2, A3– SUMPRODUCT =SUMPRODUCT(A1:A3,B1:B3)
Returns the sum of products A1B1+A2B2+A3B3– ABS =ABS(A3)
Returns the absolute value of the entry in cell A3.
Basic Excel functions and operators
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Arithmetic functions – continued – SQRT =SQRT(A3)
Returns A3– MAX =MAX(A1:A9)
Returns the Maximum of the entries in cells A1 through A9.– MIN =MIN(A1:A9)
Returns the Minimum of the entries in cells A1 through A9.
Basic Excel functions and operators
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Statistical functions– RAND() =RAND()
Generate a random number between 0 and 1 from a uniform distribution.– Probabilities and variable values under the normal distribution
NORMDIST NORMINV=NORMDIST(25,20,3,TRUE) =NORMINV(.55,20,3)Returns P(X<25) when = 20 Returns x0,, such that P(X<x0)=.55 and = 3 when = 20 and = 3
NORMSDIST NORMSMINV=NORMSDIST(1.78) =NORMSINV(.55)Returns P(Z<1.78) Returns z0, such that P(Z<z0)=.55
Basic Excel functions and operators
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Statistical functions– Probabilities and variable values under the t- distribution
TDIST TINV=TDIST(1.5,12,1) =TINV(.05,15)Returns P(t>1.5) when =12 Returns t0,, such that
P(t<-t0)=.025 and P(t>t0)=.025
when =15.Note: =TDIST(1.5,12,2) returns P(t<-1.5) + P(t>1.5)when =12.
Basic Excel functions and operators
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Statistical functions – Other probability distributions– Poisson =POISSON(7,5,TRUE)
Returns P(X<7) for Poisson with = 5.Note: false returns the probability density P(X = 7)
– EXPONDIST =EXPONDIST(40,1/20,TRUE) Returns P(X<40) for the exponential distribution with 1/=20Note: false returns the probability density f(40)=20exp(-20(40))
Basic Excel functions and operators
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Conditional functions:– IF =IF(A4>4,B1+B2, B1 – B2)
Returns B1+B2 if A4>4, and B1 – B2 if A4
– SUMIF =SUMIF(F1:F12, “>60”,G1:G12) Returns G1+G2+…+G12 only if F1+F2+…+F12>60
Basic Excel functions and operators
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– VLOOKUP =VLOOKUP(6.6,A1:E6,4) If the values in column A of a given table [A1:E6] are sorted (in an
ascending order), VLOOKUP finds the largest value in column A that is less than or equal to 6.6, identifies the row it belongs to, and returns the value in the fourth column that correspond to this row.
Note: If the values in column A are not sorted, =VLOOKUP(6.6,A1:E6,4,FALSE) finds the value 6.6 in column A, identifies the row it belongs to, and returns the value in the fourth column that corresponds to this row.
Basic Excel functions and operators
Using Excel Solver to Find an Optimal Solution and Analyze Results
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Using Excel Solver to Find an Optimal Solution and Analyze Results
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Using Excel Solver to Find an Optimal Solution and Analyze Results
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Using Excel Solver to Find an Optimal Solution and Analyze Results
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Using Excel Solver to Find an Optimal Solution and Analyze Results
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Space Rays ZappersDozens 320 360
Total LimitProfit 8 5 4360
Plastic 2 1 1000 <= 1000Prod. Time 3 4 2400 <= 2400
Total 1 1 680 <= 700Mix 1 -1 -40 <= 350
GALAXY INDUSTRIES
Using Excel Solver – Optimal Solution
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Using Excel Solver –Answer ReportMicrosoft Excel 9.0 Answer ReportWorksheet: [Galaxy.xls]GalaxyReport Created: 11/12/2001 8:02:06 PM
Target Cell (Max)Cell Name Original Value Final Value
$D$6 Profit Total 4360 4360
Adjustable CellsCell Name Original Value Final Value
$B$4 Dozens Space Rays 320 320$C$4 Dozens Zappers 360 360
ConstraintsCell Name Cell Value Formula Status Slack
$D$7 Plastic Total 1000 $D$7<=$F$7 Binding 0$D$8 Prod. Time Total 2400 $D$8<=$F$8 Binding 0$D$9 Total Total 680 $D$9<=$F$9 Not Binding 20$D$10 Mix Total -40 $D$10<=$F$10 Not Binding 390
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Using Excel Solver –Sensitivity ReportMicrosoft Excel Sensitivity ReportWorksheet: [Galaxy.xls]Sheet1Report Created:
Adjustable CellsFinal Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease$B$4 Dozens Space Rays 320 0 8 2 4.25$C$4 Dozens Zappers 360 0 5 5.666666667 1
ConstraintsFinal Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease$D$7 Plastic Total 1000 3.4 1000 100 400$D$8 Prod. Time Total 2400 0.4 2400 100 650$D$9 Total Total 680 0 700 1E+30 20$D$10 Mix Total -40 0 350 1E+30 390
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Solver – Infeasible Model
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Solver – Unbounded solution
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Solver does not alert the user to the existence of alternate optimal solutions.
Many times alternate optimal solutions exist when the allowable increase or allowable decrease is equal to zero.
In these cases, we can find alternate optimal solutions using Solver by the following procedure:
Solver – An Alternate Optimal Solution
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Observe that for some variable Xj the Allowable increase = 0, orAllowable decrease = 0.
Add a constraint of the form:Objective function = Current optimal value.
If Allowable increase = 0, change the objective to Maximize Xj
If Allowable decrease = 0, change the objective to Minimize Xj
Solver – An Alternate Optimal Solution
