Mathematics for Business Decisions, Part I
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 [pic], to compute [pic] 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 [pic] and [pic] respectively.
Problem 2 Use the methods of Marginal Analysis to plot the marginal cost function, [pic], and the marginal revenue function, [pic], on the same set of axes.
Problem 3 (i) Use the methods of Marginal Analysis to plot [pic]. (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 [pic]. (ii) How does this value relate to your work in Problem 3?
Problem 5 Let [pic]. 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 [pic] and [pic] 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 [pic] and [pic] respectively.
Problem 7 Use Differentiating.xls to plot marginal cost, [pic], over the interval from 0 to 1,500.
Problem 8 (i) Use Differentiating.xls to plot marginal profit, [pic], 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 [pic]. Hint: This value of q might not be an integer.
Problem 9 (i) Use Differentiating.xls to plot marginal revenue, [pic], over the interval from 0 to 1,500. (ii) Experiment with the Computation boxes to find a value for q at which [pic].
Problem 10 If [pic], find a formula for [pic].
Problem 11 Let [pic] and suppose that [pic]. What is [pic]?
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, [pic], 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, [pic], for audio speakers has been considered in previous exercises. The corresponding revenue function is given by [pic]. (i) Use Differentiating.xls to plot [pic] and use Graphing.xls to plot the function [pic]. (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 [pic] at the point, [pic] 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 [pic].
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