# using pseudocode 
       # possible problem instances,  
      initialize algorithm_result = 1.
      check algorithm 
      f(solution) =? initial product
      check_sum = a+b+c+d+e  
      set answers and printout with resulting values 
      pseudocode: need test cases > small,medium, giant 
      pseudocode: need testcases within range of expected operation.
      pseudocode: are there any cases too small or large to be solved?

        # pretty print from autoindent and ased editor
        # Cost Price Markup calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 2mar2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {cost price units :} }
        lappend names {markup percent:}
        lappend names {sticker discount: }
        lappend names {number of items sold: }
        lappend names {answers: mark_up units:}
        lappend names {profit on one item units : }
        lappend names {total profits on all items units: }
        lappend names {sticker price units :} 
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Calculator for Cost Price Markup
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg } 
       proc ::tcl::mathfunc::precision {precision float}  {
            #  tcl:wiki:Floating-point formatting, [AM]
            set x [ format "%#.5g" $float ]
            return $x
           }   
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ]
            set side6 $side1
            set side7 $side2
            set cost_price $side1
            set mark_up_percent $side2
            set discount_percent $side3
            set total_items_sold $side4
            set marked_price [* $cost_price [/ [+ 100. $mark_up_percent [* -1. $discount_percent] ] 100. ]]
            set mark_up_units  [* $cost_price [/  $mark_up_percent 100. ]]
            set discount_units [* $cost_price [/  $discount_percent 100. ]]
            set profit_units [- $marked_price $cost_price]
            set total_profits_units [* $profit_units $total_items_sold ]
            set side5 $mark_up_units
            set side6 $profit_units
            set side7 $total_profits_units
            set side8 $marked_price 
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |&"
            puts "&| $side1 :|cost price units  |   |&"
            puts "&| $side2 :|markup percent   | |& "  
            puts "&| $side3 :|sticker discount | |& "
            puts "&| $side4 :|number of items sold | |&"
            puts "&| $side5 :|answers: mark_up units  | |&"
            puts "&| $side6 :|profit on one item units |  |&"
            puts "&| $side7 :|total profits on all items units |  |&"
            puts "&| $side8 :|rounded sticker price units |  |&" 
            puts "&| [ ::tcl::mathfunc::precision 5 $side8] :|sticker price units |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { set side8 0 ; calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 100.0  50.  10.0 10.0  50.0  40.   400.0  140.0}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 50.0 50.0 10.0 10.00  25.0  20.0 200.0  70.0}
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 1000.0 50.0 10.0 10.0  500.0  400.0 4000.0 1400.0}
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
               . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Cost Price Markup Calculator"   
        # end of deck    

  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  

     #Pseudocode
      weighted mean3 formula   =( norm1  +  norm2 ) / ( norm1 / rate1  + norm2 / rate2 )
     set weighted_mean3 [ expr {(norm1+norm2)/((norm1/rate1)+(norm2/rate2)) }]
     set weighted_mean3 [/ [+ norm1 norm2 ] [+ [/ norm1 rate1 ] [/ norm2 rate2 ]]] 
     set weighted_mean3 [/ [+ $norm1 $norm2 ] [+ [/ $norm1 $rate1 ] [/ $norm2 $rate2 ]]] 
     same result as ( delta quantity)  / (delta time)
     set weighted_mean4 [ expr { ( $norm2-$norm1 )/(( $norm1/$rate1 )+( $norm2/$rate2 )) } ]