FINAL ASSIGNMENT Code 4 Program IB, AC, MIS, BDA Course Code MAT 1092 Course Title Advanced Mathematics Time allowed 24 hours Date 1462021 1562021 Starting at 9 00, 1462021 Ending at 9 00, 1562021 Lecturer’s Signature Date 2652021 Department’s Signature Date 52021 Instructions to students 1 At 9 00 AM, 1462021, each student is assigned a final assignment with code number that is identical to the last digit of his her student code (for example if a student code is 17071365 the las.
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Code: 4
Program: IB, AC, MIS, BDA
Course Code: MAT 1092
Course Title: Advanced Mathematics
Time allowed: 24 hours
Date: 14/6/2021 - 15/6/2021
Starting at 9:00, 14/6/2021
Ending at 9:00, 15/6/2021
Lecturer’s Signature
Date: 26/5/2021
Department’s Signature
Date: …/5/2021
Instructions to students:
1 At 9:00 AM, 14/6/2021, each student is assigned a final assignment with code number that is
identical to the last digit of his / her student code (for example: if a student code is 17071365 the
last digit is 5, and he / she must choose to do Final Assignment MAT1092 Code 5)
2 Final assignment consists of 5 problems, students should write the answers by hand to these problems in 10 pages Solution of problem 1 is written in pages 1-2, problem 2 in pages 3-4, problem 3 in pages 5-6, problem 4 in pages 7-8, problem 5 in pages 9-10 Each page is numbered clearly by hand writing in the right-top corner Some pages not used are left with blank space Students should write clearly his / her full name and student code in the first row of the first page
(for example: Nguyễn Văn Thao, 17007365).
3 To submit the final assignment, students use CamScanner to scan all the above 10 pages and save them to a pdf file, starting from page 1, then page 2, 3, 4, 5, 6, 7, 8, 9 and 10
4 Students should finish submitting the final assignment / the pdf file with the file name: student’s full name.MAT1092.lecturer’s name (for example: Nguyen_Van_Thao.MAT1092.Thanh) in
due time through MS Teams Assignment (do not be late in submitting the final assignment, since
the final assignment can not be submitted after the due time, 9:00AM, 15/6/2021)
5 Any violation of the above instructions will CAUSE ZERO MARK for the final assignment.
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Problem 1 (2 points): A manufacturer produces two models of racing bike, A and B, each of which must be processed through two machine shops Machine shop 1 is available for 92 hours per month and machine shop 2 for 134 hours per month The manufacture of each bike of type A takes 6 hours in shop 1 and 4 hours in shop 2 The corresponding times for B are 4 and 10 hours, respectively Due to a contract, the manufacturer must produce at least 5 bikes of type B per month If the profit is
$90 and $75 per bike of type A and B respectively, how should the manufacturer arrange production to maximize total profit?
Problem 2 (2 points): Consider the two-sector model:
= 0.5(C + I – Y)
C = 0.6Y + 600
I = 0.2Y + 300
a/ Find expressions for Y(t), C(t) and I(t) when Y(0) = 6500;
b/ Is this system stable or unstable, explain why?
Problem 3 (2 points): A project requires an initial outlay of $92000 and produces a return of $30000 at the end of year 1, $40000 at the end of year 2, and $42xyz at the end of year 3, where x, y, z are the last three digits of your student code (for example: if a student code is 17071365 then x = 3, y = 6, z = 5 and $42xyz=$42365) a/ Use the trial-and-error method or another appropriate method to determine the internal rate of return IRRof the project (express IRR in percentage, rounded to one decimal place);
b/ Find the net present value NPV of the project if the market rate r is equal to the value of IRR as found above, then give a comment
Problem 4 (2 points): An annuity pays out $3000 at the beginning of each year in perpetuity If the interest is 6% compounded annually, find:
a/ The present value of the whole annuity;
b/ The present value of the annuity for payments received, starting from the end of
20 th year.
Problem 5 (2 points): Consider the optimization problem of maximizing Cobb– Douglas production function: Q = 20 K 1/2 L 1/2 , subject to cost constraint: K + 4L = 64 a/ Use the method of Lagrange multipliers to find the maximum value of the production function;
b/ Estimate the change in the optimal value of Q if the cost constraint is changed to: K + 4L
= 65, and state the new maximum value of the production function.