Mathematics for Business Decisions, Part IIHomework 4Mathematics for Business Decisions, Part IIHomework 4forMath 115b, Section: Instructor: James BarrettDate: byTeam: We, the undersigned, maintain 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. Name Typed Signature % of Grade__________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ _____________________________ ____________1. A shipping company limits the circumference of its boxes to at most 80 inches with the sum of their dimensions to be at most 150 inches. (i) Modify Shipping.xls and use Solver to find the dimensions of the box with the maximum volume that will be accepted by the second company. (ii) What is the maximum volume of a box that the second company will ship?Solution:2. Condisder the situation where the demand and cost function for a certain model of audio speaker are: D(q) = -.00006q2 + 250 and C(q) = 60000 + 100q (i) Use differentiating.xlsm to plot profit, P(q) and marginal profit, P’(q). (ii) Use Solver to find a value for q that maximizes profit. (iii) Use Solver to find a value of q at which P’(q) = 0.Solution:3. In Differentiation, we considered the function C(t ) which gives the total yearly expense of purchasing and storing floppy drives, if drives are ordered every t days starting from the first day of the year.C(t )=438 , 000t+1 , 000 , 000+250⋅tUse Solver to find the value of t that minimizes C(t ).Soluton:4. (i) Use Solver and your team’s data to check your earlier numerical results. (ii) Modify your project files and use Solver to answer your team’s Questions . Question 4. How sensitive is profit to changes in price?Note: sensitivity results if the percent change in profit is more than the percent change in price. Do price changes of ±1% and ±10%.6. What profit could be expected if your product had the following price? 7. What would be the effect on profit if demand changed by the following? 8. How would the change in demand effect the optimal price of the product? 9. What would be the effect on profit if marginal costs changed by the following? Solution:5. (i) Use Graphing.xlsm to plot f =1√2 π⋅e−0 .5⋅x2 over the interval (-5,5) and usethis plot to estimate the area under the graph of f. (ii) Create a new Excel file that computes S1000( f ,[−5,5 ]) Show chart similar to text example. (iii) Based upon this computation, what do you think is the area under the graph of f, above the x-axis, and over [−5,5 ]? (iii) Do you think that it is likely, or unlikely, that f is a probability density function? Justify your answer.Solution:6. (i) Use Midpoint Sums.xls to plot f (x )= 3⋅x2 over the interval [0,2 ], and compute Sn(f ,[ 0,2 ]) for n=5, 10, 100, and 500. (ii) Use your results from Part (i) to guess the exact value of ∫023⋅x2dx. (iii) Experiment with the interval[0 , v ] for several values of v, and use the method of Parts (i) and (ii) to guess the exact value of ∫0v3⋅x2dx.Solution:7. (i) Use Midpoint Sums.xls to plot f (x )=√1−x2 over the interval [−1,1 ], and compute Sn(f ,[−1,1 ]) for n=40 and 480. (ii) Noting that the graph of f is the upper half of a circle with radius r=1, explain the sum that you found forn=480. Hint: The area of a disk with radius one is πsquare
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