We work with the function exam$\_$percentage$\_$rule, which implements the computation of your exam

percentage according to our syllabus. Implement the function using a LAMBDA:

LAMBDA$($TH$,$E$\_1,$E$\_2,$M$\_1,$M$\_2,$LET$(...))$

The connection to the syllabus should be easy: TH $($Take Home$),$ E$\_1($Exam $1),$ E$\_2($Exam $2),$ M$\_1$

$($Makeup $1),$ M$\_2($Makeup $2).$ In each exam, you can make between $0$ and $100$ points. Please carefully

review the relevant parts of the syllabus, which serves as specification for what needs to be implemented.

Your function must use the MAX function to implement the rule regarding TH and E$\_1.$

Could you implement the following versions of function exam$\_$percentage$\_$rule?

$$ OneStep version. The function works correctly for one student.

$$ Manual ManySteps version. The function works correctly for five students by dragging down the

OneStep formula five rows.

$$ Automatic ManySteps version using MAP. Fill out the Function Recipe only for this corrected

solution. The function must work correctly for any number of students. This is intended for a large

MOOC class that might have $500$ students. The following function $$almost$$ solves the problem but

requires a correction.

$=$LAMBDA$($TH$,$E$\_1,$E$\_2,$M$\_1,$M$\_2,$LET$($

COMMENT$0,$"Calculate exam percentage many students $($weighted percentage$)",$

COMMENT$1,$"Function for make$-$up exam rule. make$-$up exam $=0$ means: exam not taken",

override,LAMBDA$($exam$,$mu$\_$exam, IF$($mu$\_$exam$=0,$exam,mu$\_$exam$)),$

exam$\_$weights, $\{0\mathrm{.}06,0\mathrm{.}25,0\mathrm{.}25\},$

TH$\_$real,MAX$($TH$,$E$\_1),$

TH$\_$real$\_1,$MAP$($TH$,$E$\_1,$LAMBDA$($t$,$e$,$MAX$($t$,$e$))),$

TH$\_$real$\_2,$IF$($E$\_1>$TH$,$E$\_1,$TH$),$

E$\_1\_$real,override$($E$\_1,$M$\_1),$

E$\_2\_$real,override$($E$\_2,$M$\_2),$

unweighted$\_$exam$\_$percentages,HSTACK$($TH$\_$real,E$\_1\_$real,E$\_2\_$real$),$

weighted,exam$\_$weights$*$unweighted$\_$exam$\_$percentages,

result,BYROW$($weighted$,$LAMBDA$($row$,$SUM$($row$))),$

ShowHeader,HSTACK$("$exam$\_$weights","","","TH$\_$real","E$\_1","$E$\_2",$"weighted","","","result"$),$

Show, IFERROR$($VSTACK$($

ShowHeader,

HSTACK$($

IFERROR$($exam$\_$weights,"exam$\_$weights problem"$),$

IFERROR$($TH$\_$real,"TH$\_$real problem"$),$E$\_1\_$real,E$\_2\_$real,weighted,

IFERROR$($result$,$"result problem"$))),""),$

Show$))($GradeT$[$TH$],$GradeT$[$E$\_1],$GradeT$[$E$\_2],$GradeT$[$M$\_1],$GradeT$[$M$\_2])$

Our task is to write a function that computes the grade for any number of students without using dragging.

In this situation, we need to look for non$-$spilling functions like MAX, MIN, SUM, AND, OR that are

aggregators, i$.$e$.,$ they produce one output. We have multiple options available.

$$ Use the MAP function to reduce the problem to single$-$cell arguments.

$$ Rewrite the function so that it becomes spilling. For example, AND$($a$,$b$)$ can be rewritten as a $$b $=1,$

which is spilling. TRUE has value $1$ and FALSE has value $0.$

$$ Use BYROW and HSTACK to apply the function row by row. But this has limitations$.$

Create a worksheet called Exam Percentages and put all three versions of the function exam$\_$percentage$\_$rule

in it$.$ Create the Excel table GradeT given below. For the first version use the first row of GradeT. For

the second version use all $5$ rows through dragging. For the third version, give all $5$ rows as input.

TH E$\_1$ E$\_2$ M$\_1$ M$\_2$

$100085100100$

$0100100$

$508090100100$

$050$

$5010095$

Test your solution carefully. For table GradeT, the output should be:

$56$

$56$

$54\mathrm{.}8$

$15\mathrm{.}5$

$54\mathrm{.}75$

Note that $44\%$ are allocated for the non$-$exam grade