{"text_format":"3","workbook":"xlsx","n_sheets":5,"sheets":["Rectangle","Existing wall","Two Pens","Three Pens","Calcs"],"not_rendered":{"charts":12,"images":8,"macros":1,"defined_names":25,"comments":4},"read":"whole","date_system":"1900"}

{"sheet":"Rectangle","index":0,"n_rows":51,"n_cols":16,"rows_kept":51,"merged":[[44,2,44,3]]}
[null,"Area of a Farmer's Pen Problem"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"  the problem of finding the dimensions"]
[null,"         of the largest rectangular pen"]
[null,"           that a farmer can construct"]
[null,"     given the length of fencing to be used."]
[]
[]
[]
["What is the perimeter (length L of fencing)?"]
[null,"          (200 - 1000 feet)",null,null,"Length L =",{"$f":"10*D13+200","v":680}]
[{"$nulls":3},48,{"$f":"#REF!+D13*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
["The perimeter of the pen is L = 2x + 2y =",{"$nulls":3},{"$f":"perim0","v":680}]
["    The formula for the area function A =",{"$nulls":3},"½x(L - 2x)"]
{"$rows_empty":10}
[{"$nulls":10},"Select the amount of L used for x is",{"$nulls":3},{"$f":"IF(N29<=perim0/2,N29,perim0/2)","v":292},"feet"]
[]
[{"$nulls":13},292,{"$f":"Calcs!E7+N29*(Calcs!E8-Calcs!E7)/100","v":0}]
[]
[{"$nulls":11},"So the associated value for y = ",null,null,{"$f":"(perim0-2*x0)/2","v":48}]
[]
[{"$nulls":11},"The area of this pen is then A =",null,null,{"$f":"x0*(perim0-2*x0)","v":28032},"square feet"]
[]
[{"$nulls":11},"    The value of the derivative is A' = ",{"$nulls":3},{"$f":"L/2-2*x0","v":-244}]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Existing wall","index":1,"n_rows":53,"n_cols":14,"rows_kept":53,"merged":[[46,2,46,3]]}
[null,"Area of a Farmer's Pen Problem"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"  the problem of finding the dimensions"]
[null,"           of the largest rectangular pen"]
[null,"           that a farmer can construct"]
[null,"    using an existing fence or wall or river"]
[null,"     given the length of fencing to be used."]
[]
[]
[]
["What is the perimeter (length L of fencing)?"]
[null,"          (200 - 1000 feet)",null,null,"  Length L =",{"$f":"10*D14+200","v":900}]
[{"$nulls":3},70,{"$f":"#REF!+D14*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
["The perimeter of the pen is L = x + 2y =",{"$nulls":3},{"$f":"perim0","v":680}]
["    The formula for the area function A =",{"$nulls":3},"½x(L - x)"]
[]
[]
[]
[]
[]
[]
[{"$nulls":8},"Select the amount of L used for x is",{"$nulls":3},{"$f":"IF(L26<=perim1,L26,perim1)","v":522},"feet"]
[]
[{"$nulls":11},522,{"$f":"Calcs!B7+L26*(Calcs!B8-Calcs!B7)/100","v":0}]
[]
[{"$nulls":9},"So the associated value for y = ",null,null,{"$f":"(perim1-x00)/2","v":189}]
[]
[{"$nulls":9},"The area of this pen is then A =",null,null,{"$f":"x00*M28","v":98658},"square feet"]
[]
[{"$nulls":9},"    The value of the derivative is A' = ",{"$nulls":3},{"$f":"L/2-2*x00","v":-704}]
{"$rows_empty":7}
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Two Pens","index":2,"n_rows":50,"n_cols":13,"rows_kept":50,"merged":[[43,2,43,3]]}
[null,"Area of a Farmer's Pen Problem"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"    the problem of finding the dimensions"]
[null,"      of two equal sized rectangular pens"]
[null,"           that a farmer can construct"]
[null,"     given the length of fencing to be used."]
[]
[]
[]
["What is the perimeter (length L of fencing)?"]
[null,"          (200 - 1000 feet)",null,null,"Length L =",{"$f":"10*D13+200","v":850}]
[{"$nulls":3},65,{"$f":"#REF!+D13*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
["The perimeter of the pen is L = 3x + 2y =",{"$nulls":3},{"$f":"perim2","v":850}]
["      The formula for the area function A =",{"$nulls":3},"½x(L - 3x)"]
{"$rows_empty":8}
[{"$nulls":7},"Select the amount of L used for x is",{"$nulls":3},{"$f":"IF(K27<=perim2/3,K27,perim2/3)","v":61},"feet"]
[]
[{"$nulls":10},61,{"$f":"Calcs!B7+K27*(Calcs!B8-Calcs!B7)/100","v":0}]
[]
[{"$nulls":8},"So the associated value for y = ",null,null,{"$f":"(LLL-3*x000)/2","v":333.5}]
[]
[{"$nulls":8},"The area of the two pens is  A =",null,null,{"$f":"x000*(perim2-3*x000)","v":40687},"square feet"]
[]
[{"$nulls":8},"    The value of the derivative is A' = ",{"$nulls":3},{"$f":"LLL/2-2*x000","v":303}]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Three Pens","index":3,"n_rows":52,"n_cols":14,"rows_kept":52,"merged":[[45,2,45,3]]}
[null,"Area of a Farmer's Pen Problem"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"    the problem of finding the dimensions"]
[null,"     of three equal sized rectangular pens"]
[null,"           that a farmer can construct"]
[null,"     given the length of fencing to be used."]
[]
[]
[]
["What is the perimeter (length L of fencing)?"]
[null,"          (200 - 1000 feet)",null,null,"Length L =",{"$f":"10*D13+200","v":860}]
[{"$nulls":3},66,{"$f":"#REF!+D13*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
["The perimeter of the pen is L = 4x + 2y =",{"$nulls":3},{"$f":"llll","v":860}]
["      The formula for the area function A =",{"$nulls":3},"½x(L - 4x)"]
{"$rows_empty":10}
[{"$nulls":8},"Select the amount of L used for x is",{"$nulls":3},{"$f":"IF(K29<=perim3/4,K29,perim3/4)","v":108},"feet"]
[]
[{"$nulls":10},108,165,{"$f":"Calcs!C7+L29*(Calcs!#REF!-Calcs!C7)/100","v":{"$error":"#REF!"}}]
[]
[{"$nulls":9},"So the associated value for y = ",null,null,{"$f":"(llll-4*x0000)/2","v":214}]
[]
[{"$nulls":9},"The area of the three pens is A =",null,null,{"$f":"x0000*(perim3-4*x0000)/2","v":23112},"square feet"]
[]
[{"$nulls":9},"    The value of the derivative is A' = ",{"$nulls":3},{"$f":"llll/2-4*x0000","v":-2}]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Calcs","index":4,"n_rows":46,"n_cols":3,"rows_kept":46}
["1 Rectangle"]
[]
["Three points"]
[0,0,{"$f":"L/2-2*A4","v":340}]
[{"$f":"perim0/4","v":170},{"$f":"A5*(perim0-2*A5)/2","v":28900},{"$f":"L/2-2*A5","v":0}]
[{"$f":"perim0/2","v":340},0,{"$f":"L/2-2*A6","v":-340}]
[]
["Point on curve",null,"A'"]
[{"$f":"x0","v":292},0,0]
[{"$f":"x0","v":292},{"$f":"A9*(perim0-2*A9)/2","v":14016},{"$f":"L/2-2*x0","v":-244}]
[]
[]
["2 Existing Fence"]
[]
["Three points"]
[0,0,{"$f":"LL/2-A16","v":450}]
[{"$f":"perim1/2","v":450},{"$f":"A17*(perim1-A17)/2","v":101250},{"$f":"LL/2-A17","v":0}]
[{"$f":"perim1","v":900},0,{"$f":"LL/2-A18","v":-450}]
[]
["Point on curve",null,"A'"]
[{"$f":"x00","v":522},0,0]
[{"$f":"x00","v":522},{"$f":"A21*(perim1-A21)/2","v":98658},{"$f":"LL/2-A22","v":-72}]
[]
[]
["3.  Two Pens"]
[]
["Three points"]
[0,0,{"$f":"LLL/2-3*A28","v":425}]
[{"$f":"perim2/6","v":141.66666666666666},{"$f":"A29*(perim2-3*A29)/2","v":30104.166666666664},{"$f":"LLL/2-3*A29","v":0}]
[{"$f":"perim2/3","v":283.3333333333333},0,{"$f":"LLL/2-3*A30","v":-425}]
[]
["Point on curve",null,"A'"]
[{"$f":"x000","v":61},0,0]
[{"$f":"x000","v":61},{"$f":"A33*(perim2-3*A33)/2","v":20343.5},{"$f":"LLL/2-3*A34","v":242}]
[]
[]
["4.  Three Pens"]
[]
["Three points"]
[0,0,{"$f":"llll/2-4*A40","v":430}]
[{"$f":"perim3/8","v":107.5},{"$f":"A41*(perim3 - 4*A41)/2","v":23112.5},{"$f":"llll/2-4*A41","v":0}]
[{"$f":"perim3/4","v":215},0,{"$f":"llll/2-4*A42","v":-430}]
[]
["Point on curve",null,"A'"]
[{"$f":"x0000","v":108},0,0]
[{"$f":"x0000","v":108},{"$f":"A45*(perim3-4*A45)/2","v":23112},{"$f":"llll/2-4*A46","v":-2}]