The bookshop manager at the university has developed a matrix formula for determining the number of Pure and Applied Mathematics textbooks he should order each year. For 2016, the starting point for the formula is the column matrix. Sp. This lists the number of Pure and Applied Mathematics textbooks sold in 2015. 505 316 Pure Applied O, is a column matrix listing the number of Mathematics and Physics textbooks to be ordered for 2016. Op is given by the matrix formula : 01 = A Sp + B where A = 0.85 0 O 078 and B Determine O , correct to the nearest integer. Pure b. Given that S - 499 Applind representing the number of textbooks sold in 2016, 303 determine O2 (the numbers of books to be ordered for 2017) using the same matrix equation. The matrix formula above only allows the manager to predict the number of books he should order one year ahead. A new matrix formula enables him to determine the number of books to be ordered two or more years ahead. The new matrix formula is On+1-c0, + D where O, is a column matrix listing the number of Pure and Applied Mathematics textbooks to be ordered for year n.

The bookshop manager at the university has developed a matrix formula for determining the number of Pure and Applied Mathematics textbooks he should order each year. For 2016, the starting point for the formula is the column matrix. Sp. This lists the number of Pure and Applied Mathematics textbooks sold in 2015. 505 316 Pure Applied O, is a column matrix listing the number of Mathematics and Physics textbooks to be ordered for 2016. Op is given by the matrix formula : 01 = A Sp + B where A = 0.85 0 O 078 and B Determine O , correct to the nearest integer. Pure b. Given that S - 499 Applind representing the number of textbooks sold in 2016, 303 determine O2 (the numbers of books to be ordered for 2017) using the same matrix equation. The matrix formula above only allows the manager to predict the number of books he should order one year ahead. A new matrix formula enables him to determine the number of books to be ordered two or more years ahead. The new matrix formula is On+1-c0, + D where O, is a column matrix listing the number of Pure and Applied Mathematics textbooks to be ordered for year n.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The bookshop manager at the university has developed a matrix formula for determining the
number of Pure and Applied Mathematics textbooks he should order each year.
For 2016, the starting point for the formula is the column matrix So. This lists the number of Pure
and Applied Mathematies textbooks sold in 2015.
505
Pure
316
Applied
Oj is a column matrix listing the number of Mathematics and Physics textbooks to be ordered for
2016.
Oj is given by the matrix formula :
01 = A So + B where A= 0.85 0
0.78
80
and B =
75
Determine O1, correct to the nearest integer.
a.
Given that S, - 499
303
Pure
, representing the number of textbooks sold in 2016,
b.
Applied
determine O2 (the numbers of books to be ordered for 2017) using the same matrix
equation.
The matrix formula above only allows the manager to predict the number of books he should order
one year ahead. A new matrix formula enables him to determine the number of books to be ordered
two or more years ahead.
The new matrix formula is On + 1 -CO, +D where O, is a column matrix listing the number of
Pure and Applied Mathematics textbooks to be ordered for year n.

For this matrix equation, c-
0.85
72
and D.
0.85
50
The number of books ordered in 2015 was given by
500
Pure
Applied
Use the new matrix formula to predict, correct to the nearest integer, the number of
each Mathematics textbook the bookshop manager should order in the years
2016 – 2019 (inclusive).
d.
What do these predictions tell us about the expected popularity of these two
subjects in the forecast period ?

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