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Appendix A - Linear Programming Using the Excel Solver

APPENDIX ALINEAR PROGRAMMING USING THE EXCEL SOLVER

1. Excel Solution

X Y Total

Decision 6 0Profit $3 $1 $18

ResourcesX Y Used Capact!

A 12 14 72

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Appendix A - Linear Programming Using the Excel Solver

#.

A " Total

Decision 15 10Cost $2 $4 $70

ResourcesA " Used Capact!

A 4 6 120 >= 120B 2 6 90 >= 72C 1 10 >= 10

Graphical solution--the problem requested the Excel solution but the !ollo"ing graphicalsolution is provided !or classroom use i! desired.

A-#

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Appendix A - Linear Programming Using the Excel Solver

$. a. %aximi&e ' ( #)*1+ ,*#+ *$

s.t. *1+ #*#+ $*$ ))

/*1+ $*# /)

#*1 + *$ $#)

*$ )

*1 *# *$ 0 )

b. Excel solution

X# X$ X% Total

Decision 45 100 80Profit $20 $6 $8 $2,140

ResourcesX# X$ X% Used Capact!

Millin 8 2 3 800

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Appendix A - Linear Programming Using the Excel Solver

/. a.

Let A ( pounds o! !ood A

7 ( pounds o! !ood 7

%inimi&e 8 & ( .9A + .17

s.t. ,))A + :))7 $,)) %aximum calories

,))A + :))7 0 1)) %inimum calories

#))A + 9))7 1/)) %aximum starch

/))A + 1))7 0 /)) %inimum protein

A # %aximum amount o! A

A-/

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Appendix A - Linear Programming Using the Excel Solver

. Add constraint 1))7 1) and change ob;ective !unction to & ( 1.9A + #.)7

,. a.

Let A ( gallons o! !uel A to mix

7 ( gallons o! !uel 7 to mix

%inimi&e & ( 1.#)A + ).:)7

s.t. A + 7 0 $))) !uel demand

A + 7 /))) %aximum storage

A #))) %aximum !uel A available

7 /))) %aximum !uel 7 available

1)A - 7 0 ) 7lend ) octane minimumA + 7? 0 )

A-

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Appendix A - Linear Programming Using the Excel Solver

b.

A " Total

Decision 1000 2000 3000Cost $1'20 $'90 $3,000

ResourcesA " Used Capact!

Min %e)"n% 1 1 3000 >= 3000M"* &tor"e 1 1 3000

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Appendix A - Linear Programming Using the Excel Solver

9. Let8 ( dollars spent on !ood

S ( dollars spent on shelter

E ( dollars spent on entertainment

%aximi&e ' ( # + $S + E

s.t. + S + E 1)) 4otal 7udget

+ S 1))) %aximum on ood and Shelter

S 9)) %aximum on Shelter alone

E $)) %aximum on Entertainment

& S E Total

Decision 300 700 300

Profit 2 3 5 4,200

Resources

X# X$ X% Used Capact!

tot"l .%et 1 1 1 1300

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Appendix A - Linear Programming Using the Excel Solver

:. Cun &one !or , hours and man !or / hours at a cost o! 2$/.

,o(e Ma( Total

Decision 6 4

Cost $48 $24 $384

Processes

X# X$ Produced De-a(d

BCP1 3 1 22 >= 20BCP2 1 1 10 >= 10

BCP3 1 0 6 >= 6

1). She should plant 9)) acres in corn and 1)) acres in so3beans.

Cor( So!.ea(s /0eat Total

Decision 700 100 0 800Profit er "cre $2,000 $2,500 $3,000 $1,650,000

Resources

Cor( So!.ea(s /0eat Used Capact!

!".or orers 0'1 0'3 0'2 100