Download HW 4 - University of Arizona Math

Business Mathematics II
Homework 4
for
Math 115b, Sections:
Instructor: Ratnayaka
Due Date:
by
Team:
(Number)
We, the undersigned, affirm that each of us participated fully and equally in the completion of
this assignment and that the work contained herein is original. Furthermore, we acknowledge
that sanctions will be imposed jointly if any part of this work is found to violate the Student
Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for
this course.
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(You must provide a printout of the excel formulas used ,graphs, sample data & workings
for the problems in order to receive full credit)
Problem 1 Use Excel, with h  0.00001 , to compute MC (2,500) for buffalo dinners, rounded to
four decimal places.
Problem 2,3 and 4 refer to the situation that was discussed in problem 2 and 9 of Demand,
Revenue, Cost, and Profit hw (homework 3). The demand and cost functions for a good were
given by D(q)  0.1  q  150 and C(q)  12,000  1,300  q respectively.
Problem 2 Use the methods of Marginal Analysis to plot the marginal cost function, MC (q) ,
and the marginal revenue function, MR (q ) , on the same set of axes.
Problem 3 (i) Use the methods of Marginal Analysis to plot MP (q ) . (ii) Use your graph to
estimate the value of q that maximizes profit. (iii) What is the maximum possible profit? (iv) At
what price should the good be sold, in order to realize the maximum profit?
Problem 4 (i) Use your graphs from Problem 2 to estimate the value of q that makes
MR (q )  MC (q ) . (ii) How does this value relate to your work in Problem 3?
Problem 5 Let f ( x)  1  e  x / 2 . Use Excel and the method of Example 3 ( Example 3 is in MBD
2 Proj1.ppt(course file )-slide #81 & Example 3.xls (course file ) ) to plot both f (x ) and f (x) over
the interval from 0 to 10.
Problem 6 Use Differentiating.xls to redo Part (i) of Problem 3.
Problems 7, 8 and 9 refer to the situation that was discussed in Problem 2 & 9 of Demand,
Revenue, Cost, and Profit hw (hw 3). The demand and cost functions for a good were given by
D(q)  0.1  q  150 and C(q)  12,000  1300  q respectively.
Problem 7 Use Differentiating.xls to plot marginal cost, C (q ) , over the interval from 0 to
1,500.
Problem 8 (i) Use Differentiating.xls to plot marginal profit, P (q ) , over the interval from 0 to
1,500. (ii) Experiment with the Computation boxes to find a value for q that is greater than 100,
and at which P (q )  0 . Hint: This value of q might not be an integer.
Problem 9 (i) Use Differentiating.xls to plot marginal revenue, R (q ) , over the interval from 0
to 1,500. (ii) Experiment with the Computation boxes to find a value for q at which R (q )  0 .
Problem 10 If f ( x)  0.75  x  1.94 , find a formula for f (x) .
Problem 11 Let f ( x)  3  g ( x)  12 and suppose that g ( x)  2 . What is f (5) ?
Problem 12 When 12,000 mountain bicycles are being produced and sold the marginal revenue
is $895 and the marginal cost is $787. (i) What is the marginal profit at this production level?
(ii) What does this number mean in terms of bicycles and dollars?
Problem 13 A demand function, D(q)  0.8  q  200 , gives the price (in dollars) at which q
items can be sold. (i) Find a formula for the marginal demand. (ii) Relate your formula to
dollars and items.
Problem 14 The demand function, D(q)  0.00006  q 2  250 , for audio speakers has been
considered in previous exercises. The corresponding revenue function is given by
R(q)  q  D(q)  0.00006  q 3  250  q . (i) Use Differentiating.xls to plot R (q ) and use
Graphing.xls to plot the function g (q)  0.00018  q 2  250 . (ii) What do your plots suggest
about the form of the marginal revenue function?
*Problem 15(i) Use your team’s data to plot MR, MC, and MP for its product. (ii) Prepare
computational cells, as in the sheet Marginal of Marketing Focus.xls and use these to answer
your team’s Questions 1-3 for its product. Use the same units as in the work on the class project
in Marketing Focus.xls.
Problem 16 (i) Find the slope of the graph of f ( x)  2 x at the point, (1, f (1)) and (ii) find an
equation for the tangent line at that point. (iii) Use Excel to show both the graph of f and the
graph of the tangent line in a single plot. Plot both functions over the interval [0,3] .