modelCourse_Business_Calculus.tar

course_info.txt0000644000004100000410000000043612170303667014172 0ustar  www-datawww-dataA one semester course in differential and integral calculus with applications tuned to
business and economics.  No knowledge of Trigonometry is required. The prerequisite could be a traditional Precalculus or College Algebra course which includes exponential and logarithmic functions.
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$BBOLD Set 08: Higher order derivatives $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Use prior derivative rules (power, chain, quotient, etc.) to find higher order derivatives.
  $ITEM Understand that the first and second derivatives of position (along a straight path) give velocity and acceleration, resp.
  $ITEM Interpret changes in speed in terms of positive/negative first and second derivatives.
  $ITEM Identify where object (along a straight path) is speeding up/slowing down.

  \{EndList("UL")\}

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$HR

$PAR

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\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

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$PAR $BCENTER

$BBOLD Set 09: Marginals differentials and estimation $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Understand that marginal cost/revenue/profit can be found using a derivative. 
  $ITEM Find marginal cost/revenue/profit function and evaluate function at a point.
  $ITEM Use derivative to estimate cost/revenue/profit of (n+1)st item; compute actual cost/revenue/profit of (n+1)st item.
  $ITEM Use a differential to estimate change in cost/revenue/profit.

  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

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$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

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$PAR $BCENTER

$BBOLD Set 10: Implicit differentiation and related rates $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Use implicit differentiation to solve for dy/dx.
  $ITEM Execute implicit differentiation to find value of dy/dx at a point and the slope of a tangent line at a point. 
  $ITEM Apply implicit differentiation to related rates problem in a business context (profit, demand, etc.) 


  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

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$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

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$PAR $BCENTER

$BBOLD Set 13: Elasticity of demand  $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Compute the elasticity of demand at a given price.
  $ITEM Classify the elasticity of demand as elastic, inelastic, or unitary.
  $ITEM Decide if price should be raised or lowered by using elasticity of demand.
  $ITEM Use elasticity of demand to determine maximum revenue.

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$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

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$PAR $BCENTER

$BBOLD Set 07: The chain rule $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Find the derivative of functions using the chain rule.
  $ITEM Find the derivative of functions which require using chain rule plus the product or quotient rule.


  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

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$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

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\noindent{\large \bf {Assignment \{protect_underbar($setNumber)\}  due $formatedDueDate}}
\par\noindent \bigskip
% Uncomment and edit the line below if this course has a web page. Note that this is a comment in TeX mode.
%See the course web page for information http://yoururl/yourcourse

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Here's the list of 
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 which WeBWorK understands.
$BR
EOT

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$PAR $BCENTER

$BBOLD Set 11: Differentiation and properties of curves $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Determine intervals of increasing/decreasing behavior by analyzing the sign of the derivative.
  $ITEM Identify locations and values of relative maxima and minima.
  $ITEM Determine intervals of concavity by using the second derivative.
  $ITEM Identify locations of inflection points.
  $ITEM Draw conclusion about signs of derivatives by looking at the graph of a function.
  $ITEM Apply the above to mathematical models involving cost/revenue/profit.


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$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

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\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

$PAR

END_TEXT

ENDDOCUMENT();local/setnew_InventoryCosts/0002755000004100000410000000000012170054564016604 5ustar  www-datawww-datalocal/setnew_InventoryCosts/InventoryCosts1.pg0000644000004100000410000000602612170054740022224 0ustar  www-datawww-data# DESCRIPTION
# Minimize inventory cost problem, common to Business Calculus
# ENDDESCRIPTION

## Tagged by tbf 06/18/13

## DBsubject(Calculus - single variable)
## DBchapter(Applications of Differentiation)
## DBsection(Optimization - business and economics)
## Author(Tim Flowers)
## Level(5)

## KEYWORDS('calculus', 'derivative', 'optimization', 'inventory cost')


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TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(3,12,1);
$d = random(1,5,1);
$q = random(2,7,1);
$e = random(2,20,1);

$b = Real("2*$q");

$n = Real("4*$a*$b");		# total number for year
$h = Real("$d*$q");		# storage/holding costs
$r = Real("$a*$d");		# fixed reorder cost
$p = Real("$e");		# variable handling costs

$soln = Real("4*$a");		# lot size (solution)

$cost = Formula("($h/2)x + ($r*$n)/x + $p*$n")->reduce;


Context()->texStrings;
BEGIN_TEXT


The showroom manager of a dealership knows that they will sell $n mopeds over 
the course of an entire year.  Their cost to store a moped for an entire year 
is $DOLLAR$h.  To reorder mopeds from their supplier, there is a fixed reordering cost of $DOLLAR$r and a $DOLLAR$p handling charge for each moped ordered.  How often should the manager order mopeds, and in what lot size, in order to minimize the inventory costs?
$BR$BR
Note: Use the standard assumption that for a lot size \( x \), the average 
inventory is \( x/2 \).
$BR$BR
For a lot size \( x \), the total inventory cost for a year is given by the 
function:
$BR
\( C(x) \) = \{ ans_rule(40) \}
$BR$BR
What lot size will minimize inventory costs? 
$BR
lot size = \{ ans_rule(25) \} mopeds
$BR$BR
How many times during the year should the manager reorder mopeds?
$BR
number of orders = \{ ans_rule(25) \}

END_TEXT
Context()->normalStrings;


ANS($cost->cmp);
ANS($soln->cmp);
ANS($b->cmp );

Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
$PAR SOLUTION $PAR

There are two types of inventory costs to consider:  the holding/storage 
costs and the reorder/handling costs.  The total holding costs will be the 
number of mopeds stored, on average, for an entire year times the cost to 
store each.  This gives \( (x/2) $h \).  The cost of each order will be 
\( \$ \) $r plus \( \$ \) $p for each moped ordered.  So, one order costs 
\( ($r + $p x) \).  This needs to be multiplied by the total number of 
orders placed during the year, which is the total needed during the year divided 
by the number ordered each time or the lot size: \( $n/x \).  Thus,
$PAR
\( C(x) =  $h*(x/2) + ($r + $p*x)*($n/x) = ($h/2)x + ($r*$n)/x + $p*$n \).
$PAR
To minimize we need the derivative, \( C^{\prime}(x) = $h/2 - ($r*$n)/x^2 \).  Set 
this equal to zero and solve for \( x \) to get \( x = $soln \).
$PAR
Thus, to minimize inventory costs, the lot size should be $soln mopeds and the 
manager should place \( $n/$soln = $b\) orders.

END_SOLUTION
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$PAR $BCENTER

$BBOLD Set 05: The power rule and differentiation $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Calculate the derivative of linear and polynomials functions.
  $ITEM Recognize power functions written in rational or radical form and then implement the power rule to find their derivatives.
  $ITEM Evaluate derivatives at a point.
  $ITEM Find the slope and equation of a tangent line of given function.
  $ITEM Apply the above to cost/revenue/profit applications.


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$PAR

$HR

$PAR

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$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

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$PAR $BCENTER

$BBOLD Set 12: Optimization of Business Models $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Use derivatives to find minimum cost and maximum revenue/profit.
  $ITEM Use pricing information to find cost/revenue/profit functions and then optimize (including cost of materials and inventory costs).
  $ITEM Find the extreme values of an economic model on a closed interval.

  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

$PAR

$HR

$PAR

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$PAR

END_TEXT

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$PAR $BCENTER

$BBOLD Set 04: The derivative $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Compute the average rate of change of a function over an interval.
  $ITEM Estimate the instantaneous rate of change of a function from its graph.
  $ITEM Use the definition of the derivative to compute the derivative of simple power functions and polynomials.
  $ITEM Solve business application problems involving finding the marginal of some function using differentiation.
  $ITEM Compute the tangent line (a.k.a. best linear approximation) to the graph of a function at a point.


  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

$PAR

END_TEXT

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$PAR $BCENTER

$BBOLD Set 14: Review of exponentials and logarithms $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Identify graphs of exponential and logarithmic functions.
  $ITEM Evaluate and simplify log expressions using log properties.
  $ITEM Use the “change of base” formula to evaluate logs.
  $ITEM Apply exponential models to solve application problems.

  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

$PAR

END_TEXT

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$PAR $BCENTER

$BBOLD Set 06: The product and quotient rules $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Find the derivative of a function using the product rule.
  $ITEM Find the derivative of a function using the quotient rule.
  $ITEM Use the product and quotient rules with unspecified functions.
  $ITEM Apply the product rule in business contexts (e.g. revenue).


  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

$PAR

END_TEXT

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$PAR $BCENTER

$BBOLD Set 01: Review of Function Concepts $EBOLD

$ECENTER

$HR

$PAR

Due: $BBOLD

$formattedDueDate. $EBOLD

$PAR

$HR

Students will be able to:

   \{BeginList("UL")\}

  $ITEM Distinguish between the graphs of functions and non-functional relations.
  $ITEM Demonstrate understanding of the terminology: domain, range, independent variable, dependent variable, inverse function.
  $ITEM Determine the domain and range of functions given algebraically and graphically.  Use interval notation and inequalities to express these sets.
  $ITEM Be able to compose two functions and decompose a function into simpler components
  $ITEM Identify vertical and horizontal shifts and reflections of a given function.
  $ITEM Work with functions that are defined piecewise.
  $ITEM Translate between graphical and tabular representations of the same function.

  \{EndList("UL")\}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Available_Functions!,"Functions and symbols that WeBWorK understands.") \}

$PAR

$HR

$PAR

\{ htmlLink(qq!http://webwork.maa.org/wiki/Student_Information!,"Links to some useful WeBWorK pages for students ") \}

$PAR

END_TEXT

ENDDOCUMENT();setSet_01_Review_of_Function_Concepts.def0000644000004100000410000000362612175556121021061 0ustar  www-datawww-data
openDate          = 07/11/2013 at 10:00am EDT
dueDate           = 01/01/2020 at 07:01pm EST
answerDate        = 01/08/2020 at 07:00pm EST
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problemList       = 
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Library/LoyolaChicago/Precalc/Chap2Sec2/Q13.pg, 1, -1 
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Library/FortLewis/Algebra/8-2-Function-composition/MCH1-8-2-08-Function-composition.pg, 1, -1 
Library/FortLewis/Algebra/8-2-Function-composition/MCH1-8-2-02-Function-composition.pg, 1, -1 
Library/FortLewis/Algebra/8-2-Function-composition/MCH1-8-2-09-Function-composition.pg, 1, -1 
Library/FortLewis/Algebra/8-2-Function-composition/MCH1-8-2-10-Function-composition.pg, 1, -1 
Library/FortLewis/Algebra/8-2-Function-composition/MCH1-8-2-30-Function-composition.pg, 1, -1 
Library/Utah/College_Algebra/set6_Polynomial_and_Rational_Functions/1050s6p1/1050s6p1.pg, 1, -1 
Library/Utah/College_Algebra/set6_Polynomial_and_Rational_Functions/1050s6p10/1050s6p10.pg, 1, -1 
Library/Utah/College_Algebra/set6_Polynomial_and_Rational_Functions/1050s6p7/1050s6p7.pg, 1, -1 
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Library/Rochester/setIntegrals14Substitution/S05.05.Substitution.PTP02a.pg, 1, -1 
Library/Rochester/setIntegrals14Substitution/S05.05.Substitution.PTP13.pg, 1, -1 
Library/UCSB/Stewart5_5_5/Stewart5_5_5_61.pg, 1, -1 
Library/UCSB/Stewart5_5_5/Stewart5_5_5_58.pg, 1, -1 
Library/Michigan/Chap7Sec1/Q57.pg, 1, -1 
Library/Rochester/setIntegrals14Substitution/sc5_5_49.pg, 1, -1 
Library/Rochester/setIntegrals14Substitution/sc5_5_51.pg, 1, -1 

setSet_20_Consumer_and_Producer_Surplus.def0000644000004100000410000000100512175556121021434 0ustar  www-datawww-data
openDate          = 07/11/2013 at 10:00am EDT
dueDate           = 01/01/2020 at 07:20pm EST
answerDate        = 01/08/2020 at 07:00pm EST
paperHeaderFile   = defaultHeader
screenHeaderFile  = defaultHeader
problemList       = 
Library/Utah/Quantitative_Analysis/set12_Definite_Integrals_Techniques_of_Integration/s1p9.pg, 1, -1 
Library/Utah/Quantitative_Analysis/set12_Definite_Integrals_Techniques_of_Integration/s1p8.pg, 1, -1 
Library/Michigan/Chap8Sec6/Q15.pg, 1, -1 
Library/Michigan/Chap8Sec6/Q19.pg, 1, -1