{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Product","Sum","Calcs"],"not_rendered":{"charts":2,"images":4,"macros":1,"defined_names":14,"comments":2},"read":"whole","date_system":"1900"}

{"sheet":"Product","index":0,"n_rows":32,"n_cols":15,"rows_kept":32,"merged":[[25,2,25,3]]}
[null,"Maximum Product of Two Numbers"]
[]
[null,"     This DIGMath module lets you investigate "]
[null,"   the problem of finding two positive numbers"]
[null,"               whose product is a maximum"]
[null,"                         given their sum."]
[]
[]
["What is the sum S of the two numbers?"]
[null,"          (5 - 100 )",null,"  Sum S =",{"$f":"D11","v":50}]
[{"$nulls":3},50]
[]
["The sum of the two numbers is S = x + y =",{"$nulls":3},{"$f":"S","v":50}]
[" The formula for the product function P =",{"$nulls":3},"x(S - x) = Sx - x2"]
[{"$nulls":3},"= ",{"$f":"TEXT(S,\"0\")&\"x - x^2\"","v":"50x - x^2"},{"$nulls":5},"Select the value of x =",null,null,{"$f":"N16*dx","v":17.25}]
[{"$nulls":13},69,{"$f":"Calcs!E7+N16*(Calcs!E8-Calcs!E7)/100","v":0}]
[]
["Click each item below for suggestions and investigations",{"$nulls":9},"The associated value for y = ",{"$nulls":3},{"$f":"S-x0","v":32.75}]
[null,null,"   Item 1"]
[null,null,"   Item 2",{"$nulls":8},"  Their product is P =",null,null,{"$f":"x0*(S-x0)","v":{"v":564.9375,"d":"565"}}]
[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   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Sum","index":1,"n_rows":43,"n_cols":13,"rows_kept":43,"merged":[[25,2,25,3]]}
[null,"The Minimum Sum of Two Numbers"]
[]
[null,"     This DIGMath module lets you investigate "]
[null,"    the problem of finding two positive numbers"]
[null,"                  whose sum is a minimum"]
[null,"                     given their product."]
[]
[]
["What is the product P of the two numbers?"]
[null,"          (5 - 1000 )",null,"  Product P =",{"$f":"D11","v":700}]
[{"$nulls":3},700]
[]
["The product of the  numbers is P = x y =",{"$nulls":3},{"$f":"P","v":700}]
["    The formula for the sum function S =",{"$nulls":3},"x + P/x "]
[{"$nulls":3},"= ",{"$f":"\"x + \"&TEXT(P,\"0\")&\"/x\"","v":"x + 700/x"}]
[{"$nulls":8},"Select the value of x =",null,null,{"$f":"L17*dxx","v":14.57}]
[{"$nulls":11},47,{"$f":"Calcs!C8+L17*(Calcs!C9-Calcs!C8)/100","v":78.243125}]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1",{"$nulls":5},"The associated value for y = ",{"$nulls":3},{"$f":"P/x00","v":{"v":48.04392587508579,"d":"48.04"}}]
[null,null,"   Item 2"]
[null,null,"   Item 3",{"$nulls":6},"  Their sum is S =",null,null,{"$f":"x00+M19","v":{"v":62.61392587508579,"d":"62.61"}}]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]
{"$rows_empty":7}
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]

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