Application of Mathematics in Business

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In this study, the relationships between matrix division and some matrix properties such as transpose, simplification, and expansion are discussed. Unless otherwise stated, our matrices are real number matrices. The relationship between our definitions of column co-divisor and row co-divisor of a matrix on another matrix is examined. Equality and differences of these connections are observed. The validity of the provided features is discussed under which conditions. These features have been determined. Examples are given for features that do not. Some of the obtained properties bring different solutions to the solution of linear equation systems, which are encountered in the literature and are more used. This led us to examine the relationship between the defined division operation and transpose. Investigations on this subject enabled the presentation of new definitions, lemmas and theorems. Examination of these offered a broader perspective on the given mathematical expressions.

In this study, the relationships between matrix division and some matrix properties such as transpose, simplification, and expansion are discussed. Unless otherwise stated, our matrices are real number matrices. The relationship between our definitions of column co-divisor and row co-divisor of a matrix on another matrix is examined. Equality and differences of these connections are observed. The validity of the provided
features is discussed under which conditions. These features have been determined. Examples are given for
features that do not. Some of the obtained properties bring different solutions to the solution of linear equation systems, which are encountered in the literature and are more used. This led us to examine the relationship between the defined division operation and transpose. Investigations on this subject enabled the presentation of new definitions, lemmas and theorems. Examination of these offered a broader perspective on the given mathematical expressions.

1.Perusahaan “Smart City ” memproduksi perlengkapan rumah tangga dengan biaya tetap
sebesar $ 600.000 dan biaya variabel $ 300 per unit. Jika produknya dijual dengan harga $
500 per unit. Tentukan jumlah produk yang harus terjual agar memperoleh laba sebesar
$400.000.
Jawaban : Diketahui :
Fixed Cost : $ 600.000
Variabel Cost : $ 300.000 / unit
P (Selling Price) : $ 500.000 / unit Ditanya :
Q (jumlah produk yang harus terjual agar memperoleh laba sebesar $400.000) ? Penyelesaian :
Profit = TR-TC
$ 400.000 = (P.Q) – [Fix Cost + (VC.Q)]
$400.000 = ($500 Q) - ($600.000 + $300 Q)
$400.000 = $200 Q - $600.000
$400.000 + $600.000 = $200 Q
$1.000.000 = $200 Q
Q = 5.000 unit produk
Jadi jumlah produk yang harus terjual untuk dapat memperoleh laba sebesar $ 400.000
Adalah dengan menjual 5.000 unit produk
2. Perusahaan yang memproduksi sepatu olah raga memproduksi sepatu baru dengan biaya $60per unit. Dalam rangka mempromosikan produk barunya, perusahaan memberikan diskon sebesar 20% dari harga jualnya. Namun setelah diskon tersebut perusahaan menginginkan laba sebesar 15%. Berapa harga jual per unit yang harus ditetapkan ?
Diketahui :
Biaya produksi per unit = $60
Discount = 20% dari harga jual
Profit = 15% dari harga jual setelah discount
Ditanya :
P (atau harga jual per unit yg harus ditetapkan) ?
Jawaban :
P= P sebelum diskon (100/100) – discount (20/100)
P = Biaya produksi + Profit yang diinginkan
(80/100) P = $60 + ((15/100) x $60)
0.8 P = $60 + (0.15 x $60)
0.8 P = $60 + $9
0.8 P = $69
P = $69/0.8
P = $86.25
Jadi harga jual per unit yang harus ditetapkan sebesar $86.25

The focus of this paper is to discuss the application of mathematics to good governance. The paper explains the meaning of mathematics and good governance. It identifies application of mathematics in some of the elements of good governance, problems and significance of mathematics to good governance in some areas.

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