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An electronics firm manufacture two types of personal computers, a standard model and a portable model. The production of a standard computer requires a capital expenditure of $400 and 40 hours of labor. The production of a portable computer requires a capital expenditure of $250 and 30 hours of labor. The firm has $20,000 capital and 2,160 labor-hours available for production of standard and portable computers. b. If each standard computer contributes a profit of $320 and each portable model contributes profit of $220, how much profit will the company make by producing the maximum number of computer determined in part (A)? Is this the maximum profit? If not, what is the maximum profit?

Pertanyaan


 

An electronics firm manufacture two types of personal computers, a standard model and a portable model. The production of a standard computer requires a capital expenditure of $400 and 40 hours of labor. The production of a portable computer requires a capital expenditure of $250 and 30 hours of labor. The firm has $20,000 capital and 2,160 labor-hours available for production of standard and portable computers.

b. If each standard computer contributes a profit of $320 and each portable model contributes profit of $220, how much profit will the company make by producing the maximum number of computer determined in part (A)? Is this the maximum profit? If not, what is the maximum profit?begin mathsize 14px style space end style 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Misalkan

x equals Jenis space komputer space model space standart y equals Jenis space komputer space model space portabel

Dari soal dapat dituliskan ke dalam tabel berikut


Penulisan model matematika

Fungsi kendala:

table attributes columnalign right center left columnspacing 0px end attributes row cell 400 x plus 250 y end cell less or equal than cell 20.000 rightwards double arrow 8 x plus 5 y less or equal than 400 end cell row cell 40 x plus 30 y end cell less or equal than cell 2160 rightwards double arrow 4 x plus 3 y less or equal than 216 end cell row x greater or equal than 0 row y greater or equal than 0 end table

Fungsi tujuan

z equals 320 x plus 220 y

Penentuan titik potong masing-masing garis pembatas dengan sumbu koordinat seperti terlihat pada tabel berikut.


 

Titik potong antar garis pembatas 

table row cell 8 x end cell plus cell 5 y end cell equals 400 row cell 4 x end cell plus cell 3 y end cell equals 216 end table open vertical bar table row cell cross times 1 end cell row cell cross times 2 end cell end table close vertical bar table row blank blank blank blank blank blank row cell 8 x end cell plus cell 5 y end cell equals 400 blank row cell 8 x end cell plus cell 6 y end cell equals 432 minus row blank blank cell negative y end cell equals cell negative 32 end cell blank end table space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space y space space space equals space 32

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x plus 3 open parentheses 32 close parentheses end cell equals 216 row cell 4 x plus 96 end cell equals 216 row cell 4 x end cell equals cell 216 minus 96 end cell row cell 4 x end cell equals 120 row x equals 30 end table

Daerah himpunan penyelesaiaan
 


 

Penentuan nilai maksimum dengan uji titik pojok

table attributes columnalign right center left columnspacing 0px end attributes row z equals cell 320 x plus 220 y end cell row cell open parentheses 0 comma 54 close parentheses end cell rightwards double arrow cell z equals 220 open parentheses 54 close parentheses equals $ 11.880 end cell row cell open parentheses 30 comma 32 close parentheses end cell rightwards double arrow cell z equals 320 open parentheses 30 close parentheses plus 220 open parentheses 32 close parentheses equals $ 16.640 end cell row cell open parentheses 50 comma 0 close parentheses end cell rightwards double arrow cell z equals 320 open parentheses 50 close parentheses equals $ 16.000 end cell end table

Dengan demikian laba maksimal yang dicapai oleh perusahaan adalah $16.640

Jadi, keuntungan maksimal yang dicapai oleh perusahaan adalah $16.640

 

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