Denise Sakai Troxell (2000)

Solving Equations

with Excel Solver

for Microsoft Excel 2000

Denise Sakai Troxell (2000)

A Simple Problemgrades, grades, grades*…

You would love to have a quiz average of 80 points (or better) in the QTM1300 course by the end of the semester.

Your quiz scores on the first eight quizzes are given in the table below.

Quiz 1 2 3 4 5 6 7 8

Score 90 88 78 68 84 82 66 74

What scores do you need to earn on the 9th and 10th final quizzes in order to meet your goal average of 80 points? * from FCL Excel Notes by Joyce Gordon, Babson College, 1998.

Denise Sakai Troxell (2000)

You are looking for

x = score on 9th quiz (0 x 100)

y = score on 10th quiz (0 y 100)

so that

Formulate the Problemobtain equation to be solved

90 + 88 + 78 + 68 + 84 + 82 + 66 + 74 + x + y = 80

10

Quiz AverageQuiz Average

NOTE: When using Excel Solver to solve an equation make sure the right-hand side is a constant.

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverstart with a blank sheet

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter labels and constants

Enter labels in cells A1:A13 and

B1

Enter labels in cells A1:A13 and

B1

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter labels and constants

NOTE: These labels are not essential for the use of

Solver

NOTE: These labels are not essential for the use of

Solver

Denise Sakai Troxell (2000)

enter labels and constantsPreparing the Worksheet for Solver

Enter constants in cells B2:B9

Enter constants in cells B2:B9

Remember…

7466828468788890Score

87654321Quiz

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

Variable values in cells B10 and B11Variable values in cells B10 and B11

Left-hand side of equation in cell B13

Left-hand side of equation in cell B13

NOTE: These cells will be colored to indicate that they are essential for

Solver

NOTE: These cells will be colored to indicate that they are essential for

Solver

Remember…

90 + 88 + 78 + 68 + 84 + 82 + 66 + 74 + x + y = 80

10

xy

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

Click on cell B13Click on cell B13

Remember…

90 + 88 + 78 + 68 + 84 + 82 + 66 + 74 + x + y = 80

10

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

Type in =AVERAGE(Type in =AVERAGE(

Remember…

90 + 88 + 78 + 68 + 84 + 82 + 66 + 74 + x + y = 80

10

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

Remember…

90 + 88 + 78 + 68 + 84 + 82 + 66 + 74 + x + y = 80

10

Highlight cells B2:B11

Highlight cells B2:B11

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

Type in ) and hit Enter

Type in ) and hit Enter

Remember…

90 + 88 + 78 + 68 + 84 + 82 + 66 + 74 + x + y = 80

10

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

NOTE: Alternative formula for cell B13: =(B2+ B3+ B4+ B5+ B6+ B7+ B8+ B9+ B10+ B11)/10NOTE: Alternative formula for cell B13: =(B2+ B3+ B4+ B5+ B6+ B7+ B8+ B9+ B10+ B11)/10

Denise Sakai Troxell (2000)

Preparing the Worksheet for Solverenter formula

NOTE: The function AVERAGE entered in cell B13 returns the average of the values in cells B2:B11;

blank cells are ignored

NOTE: The function AVERAGE entered in cell B13 returns the average of the values in cells B2:B11;

blank cells are ignored

Denise Sakai Troxell (2000)

Using Solverinvoke Solver

Click on ToolsClick on Tools

Denise Sakai Troxell (2000)

Using Solverinvoke Solver

Click on SolverClick on Solver

Denise Sakai Troxell (2000)

Using Solverinvoke Solver

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Click on cell B13Click on cell B13

NOTE: The cell displayed in the Set Target Cell: box must contain the formula for the left-hand side of the equation

(cell B13)

NOTE: The cell displayed in the Set Target Cell: box must contain the formula for the left-hand side of the equation

(cell B13)

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Check the Value of: circle

Check the Value of: circle

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

NOTE: The value displayed in the Value of: box must be the constant on the right-hand side of the

equation (80)

NOTE: The value displayed in the Value of: box must be the constant on the right-hand side of the

equation (80)

Click on the Value of: box

Click on the Value of: box

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

NOTE: The value displayed in the Value of: box must be the constant on the right-hand side of the

equation (80)

NOTE: The value displayed in the Value of: box must be the constant on the right-hand side of the

equation (80)

Type in 80Type in 80

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Click on the By Changing Cells:

box

Click on the By Changing Cells:

box

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Highlight cells B10:B11

Highlight cells B10:B11

NOTE: The cells displayed in the By Changing Cells: box must be the cells containing variable values

(cells B10:B11)

NOTE: The cells displayed in the By Changing Cells: box must be the cells containing variable values

(cells B10:B11)

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Click on AddClick on Add

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Highlight cells B10:B11

Highlight cells B10:B11

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

Click on the Cell Reference: box

Click on the Cell Reference: box

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

Make sure <= is displayed

Make sure <= is displayed

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

Click on the Constraint: box and type in 100

Click on the Constraint: box and type in 100

Denise Sakai Troxell (2000)

Using Solvercomplete the Solver Parameters dialog box

Click on OKClick on OK

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x,y

100)

Denise Sakai Troxell (2000)

Using Solverset the Options

Click on OptionsClick on Options

Denise Sakai Troxell (2000)

Using Solverset the Options

Check the Assume Linear Model

and the Assume Non-

Negative boxes

Check the Assume Linear Model

and the Assume Non-

Negative boxes

NOTE: The equation (in the Target Cell B13) is linear on the non-negative variables (x in B10

and y in B11)

NOTE: The equation (in the Target Cell B13) is linear on the non-negative variables (x in B10

and y in B11)

Denise Sakai Troxell (2000)

Using Solverset the Options

Accept the remaining default options by clicking

on OK

Accept the remaining default options by clicking

on OK

NOTE: The equation (in the Target Cell B13) is linear on the non-negative variables (x in B10

and y in B11)

NOTE: The equation (in the Target Cell B13) is linear on the non-negative variables (x in B10

and y in B11)

Denise Sakai Troxell (2000)

Using Solverexecute Solver

Click on SolveClick on Solve

Denise Sakai Troxell (2000)

Using Solverread solution

You need to earn a score of 100 on the 9th quiz and 70 on the 10th quiz to meet your goal average of 80 points.

You need to earn a score of 100 on the 9th quiz and 70 on the 10th quiz to meet your goal average of 80 points.

Denise Sakai Troxell (2000)

Using Solverend execution

Click on OKClick on OK

Denise Sakai Troxell (2000)

Using Solvera final comment

NOTE: Excel Solver might not find all possible solutions

NOTE: Excel Solver might not find all possible solutions

You need algebra!

COMPLETE SOLUTION

You need to earn a score of

x on the 9th quiz,

where 70 x 100, and

170 – x on the 10th quiz

to meet your goal average of 80 points.

COMPLETE SOLUTION

You need to earn a score of

x on the 9th quiz,

where 70 x 100, and

170 – x on the 10th quiz

to meet your goal average of 80 points.