Лабораторная работа 10. Решение оптимизационных задач с

Ⱥ.Ȼ. Ƚɟɞɪɚɧɨɜɢɱ, ȼ.ȼ. Ƚɟɞɪɚɧɨɜɢɱ – Ɏɢɧɚɧɫɨɜɚɹ ɢɧɮɨɪɦɚɬɢɤɚ – Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 10
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ 10. Ɋɟɲɟɧɢɟ ɨɩɬɢɦɢɡɚɰɢɨɧɧɵɯ ɡɚɞɚɱ ɫ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ
«ɉɨɢɫɤ ɪɟɲɟɧɢɹ» ɜ MS Excel
ɐɟɥɶ ɪɚɛɨɬɵ – ɧɚɭɱɢɬɶɫɹ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɨɪɬɮɟɥɹ ɰɟɧɧɵɯ
ɛɭɦɚɝ ɫ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ.
Ʉ ɡɚɳɢɬɟ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɵ ɫɬɭɞɟɧɬ ɞɨɥɠɟɧ ɩɪɟɞɫɬɚɜɢɬɶ ɮɚɣɥɵ ɅɊ10_Ɏɚɦɢɥɢɹ.xls
ɢ Ɉɬɱɟɬ_ɅɊ10_Ɏɚɦɢɥɢɹ.doc.
ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ
Ɂɚɞɚɱɚ 1
Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɨɪɬɮɟɥɹ ɞɥɹ ɭɫɥɨɜɢɣ, ɡɚɞɚɧɧɵɯ ɧɚ ɪɢɫɭɧɤɟ 10.1:
Ɋɢɫɭɧɨɤ 10.1 – ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɡɚɞɚɱɢ ɨɩɬɢɦɢɡɚɰɢɢ
ɉɨɪɹɞɨɤ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ
Ɂɧɚɱɟɧɢɹ ɫɬɨɥɛɰɚ ɉɪɢɛɵɥɶ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɩɪɨɢɡɜɟɞɟɧɢɟ Ⱦɨɯɨɞɧɨɫɬɢ ɢ ɋɭɦɦɵ ɜɥɨɠɟɧɢɣ.
Ɂɧɚɱɟɧɢɟ ɋɭɦɦɚ ɜ ɧɚɞɟɠɧɵɯ ɚɤɬɢɜɚɯ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɫɭɦɦɭ ɜɥɨɠɟɧɢɣ, ɭ ɤɨɬɨɪɵɯ ɡɧɚɱɟɧɢɟ ɇɚɞɟɠɧɨɫɬɢ ɧɟ ɦɟɧɟɟ 4.
Ɂɧɚɱɟɧɢɟ ɋɭɦɦɚ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɚɤɬɢɜɚɯ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɫɭɦɦɭ ɜɥɨɠɟɧɢɣ, ɋɪɨɤ ɜɵɤɭɩɚ
ɩɨ ɤɨɬɨɪɵɦ ɧɚɫɬɭɩɚɟɬ ɩɨɡɞɧɟɟ 2015 ɝɨɞɚ.
Ɂɧɚɱɟɧɢɟ Ⱦɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɢɬɨɝɨɜɨɣ ɩɪɢɛɵɥɢ ɤ ɢɬɨɝɨɜɨɣ ɫɭɦɦɟ ɜɥɨɠɟɧɢɣ (ɜ %).
ɋ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɧɚɣɞɢɬɟ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ Ⱦɨɯɨɞɧɨɫɬɶ
ɩɨɪɬɮɟɥɹ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɨɝɪɚɧɢɱɟɧɢɹɯ:
a) Ɉɛɳɚɹ ɫɭɦɦɚ ɜɥɨɠɟɧɢɣ ɪɚɜɧɚ $200 000.
b) ɋɭɦɦɚ ɜɥɨɠɟɧɢɣ ɜ ɤɚɠɞɵɣ ɚɤɬɢɜ ɧɟ ɩɪɟɜɵɲɚɟɬ ɱɟɬɜɟɪɬɢ ɨɬ Ɉɛɳɟɣ ɫɭɦɦɵ ɜɥɨɠɟɧɢɣ.
c) ɋɭɦɦɚ ɜ ɧɚɞɟɠɧɵɯ ɚɤɬɢɜɚɯ ɫɨɫɬɚɜɥɹɟɬ ɧɟ ɦɟɧɟɟ 2/3 ɨɬ Ɉɛɳɟɣ ɋɭɦɦɵ ɜɥɨɠɟɧɢɣ.
d) ɋɭɦɦɚ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɚɤɬɢɜɚɯ ɫɨɫɬɚɜɥɹɟɬ ɧɟ ɦɟɧɟɟ ɩɨɥɨɜɢɧɵ ɨɬ Ɉɛɳɟɣ ɫɭɦɦɵ
ɜɥɨɠɟɧɢɣ.
ɉɊɂɆȿɑȺɇɂȿ:
1. Ⱦɥɹ ɪɚɫɱɟɬɚ ɡɧɚɱɟɧɢɣ ɋɭɦɦɚ ɜ ɧɚɞɟɠɧɵɯ ɚɤɬɢɜɚɯ ɢ ɋɭɦɦɚ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɚɤɬɢɜɚɯ ɢɫɩɨɥɶɡɭɣɬɟ ɮɭɧɤɰɢɸ ɋɍɆɆȿɋɅɂ:
ɋɢɧɬɚɤɫɢɫ ɮɭɧɤɰɢɢ:
ɋɍɆɆȿɋɅɂ(ɞɢɚɩɚɡɨɧ; ɤɪɢɬɟɪɢɣ; ɞɢɚɩɚɡɨɧ_ɫɭɦɦɢɪɨɜɚɧɢɹ)
ɞɢɚɩɚɡɨɧ – ɞɢɚɩɚɡɨɧ ɩɪɨɜɟɪɹɟɦɵɯ ɹɱɟɟɤ;
ɤɪɢɬɟɪɢɣ – ɤɪɢɬɟɪɢɣ ɜ ɮɨɪɦɟ ɱɢɫɥɚ, ɜɵɪɚɠɟɧɢɹ ɢɥɢ ɬɟɤɫɬɚ, ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɫɭɦɦɢɪɭɟɦɵɟ
ɹɱɟɣɤɢ;
ɞɢɚɩɚɡɨɧ_ɫɭɦɦɢɪɨɜɚɧɢɹ – ɮɚɤɬɢɱɟɫɤɢɟ ɹɱɟɣɤɢ ɞɥɹ ɫɭɦɦɢɪɨɜɚɧɢɹ.
2. Ⱦɥɹ ɜɤɥɸɱɟɧɢɹ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɜɵɩɨɥɧɢɬɟ ɤɨɦɚɧɞɭ ɋɟɪɜɢɫ – ɇɚɞɫɬɪɨɣɤɢ, ɜ
ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɇɚɞɫɬɪɨɣɤɢ ɫɪɟɞɢ ɞɨɫɬɭɩɧɵɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɜɵɛɟɪɢɬɟ ɉɨɢɫɤ ɪɟɲɟɧɢɹ.
ȼɵɩɨɥɧɢɬɟ ɤɨɦɚɧɞɭ ɋɟɪɜɢɫ – ɉɨɢɫɤ ɪɟɲɟɧɢɹ.
ȼ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɜ ɤɚɱɟɫɬɜɟ ɰɟɥɟɜɨɣ ɹɱɟɣɤɢ ɜɵɛɟɪɢɬɟ Ⱦɨɯɨɞ1
Ⱥ.Ȼ. Ƚɟɞɪɚɧɨɜɢɱ, ȼ.ȼ. Ƚɟɞɪɚɧɨɜɢɱ – Ɏɢɧɚɧɫɨɜɚɹ ɢɧɮɨɪɦɚɬɢɤɚ – Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 10
ɧɨɫɬɶ ɩɨɪɬɮɟɥɹ (ȿ11), ɭɫɬɚɧɨɜɢɬɟ ɟɟ ɪɚɜɧɨɣ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ.
ȼ ɤɚɱɟɫɬɜɟ ɹɱɟɟɤ ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɜɵɛɟɪɢɬɟ ɫɬɨɥɛɟɰ, ɫɨɞɟɪɠɚɳɢɣ ɡɧɚɱɟɧɢɹ ɋɭɦɦɚ ɜɥɨɠɟɧɢɣ (ȿ2:ȿ7).
Ⱦɨɛɚɜɶɬɟ ɨɝɪɚɧɢɱɟɧɢɹ a) – d) ɢ ɞɥɹ ɋɭɦɦɚ ɜɥɨɠɟɧɢɣ (ȿ2:ȿ7) – ɧɟɨɬɪɢɰɚɬɟɥɶɧɨɟ ɱɢɫɥɨ
(ɤɧɨɩɤɚ Ⱦɨɛɚɜɢɬɶ).
ɇɚɠɦɢɬɟ ɤɧɨɩɤɭ ȼɵɩɨɥɧɢɬɶ.
ɋɨɯɪɚɧɢɬɟ ɢ ɩɪɨɚɧɚɥɢɡɢɪɭɣɬɟ ɧɚɣɞɟɧɧɨɟ ɪɟɲɟɧɢɟ.
Ɂɚɞɚɱɚ 2
Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɨɪɬɮɟɥɹ ɞɥɹ ɞɚɧɧɵɯ, ɭɤɚɡɚɧɧɵɯ ɧɚ ɪɢɫɭɧɤɟ 10.2, ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɞɨɥɢ ɚɤɬɢɜɨɜ ɧɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ
ɢ ɪɢɫɤ ɧɟ ɩɪɟɜɵɲɚɟɬ 0,35.
Ɋɢɫɭɧɨɤ 10.2 – ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɡɚɞɚɱɢ 2
ɉɨɪɹɞɨɤ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ
ɉɭɫɬɶ ɩɟɪɜɨɧɚɱɚɥɶɧɵɟ ɞɨɥɢ ɚɤɬɢɜɨɜ Ⱥ, ȼ ɢ ɋ ɜ ɩɨɪɬɮɟɥɟ ɪɚɜɧɵ 0, 0 ɢ 1 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
ȼ ɹɱɟɣɤɭ F5 ɜɜɟɞɢɬɟ ɮɨɪɦɭɥɭ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɫɭɦɦɵ ɞɨɥɟɣ.
Ɉɠɢɞɚɟɦɭɸ ɞɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɪɚɫɫɱɢɬɚɣɬɟ ɜ ɹɱɟɣɤɟ ɋ6 ɩɨ ɮɨɪɦɭɥɟ:
=ɋɍɆɆɉɊɈɂɁȼ(B2:B4;F2:F4)
Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɞɢɫɩɟɪɫɢɢ ɞɨɯɨɞɚ (ɹɱɟɣɤɚ ɋ7) ɜɜɟɞɢɬɟ ɮɨɪɦɭɥɭ:
=C2*F2^2+D3*F3^2+E4*F4^2+2*F2*F3*C3+2*F2*F4*C4+2*F3*F4*D4
ɋɬɚɧɞɚɪɬɧɨɟ ɨɬɤɥɨɧɟɧɢɟ (ɪɢɫɤ) ɜɵɱɢɫɥɢɬɟ ɩɨ ɮɨɪɦɭɥɟ =ɄɈɊȿɇɖ(C7) ɢ ɩɨɦɟɫɬɢɬɟ
ɜ ɹɱɟɣɤɭ ɋ8.
ɐɟɥɟɜɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɪɢɫɤɚ (0,35) ɜɜɟɞɢɬɟ ɜ ɹɱɟɣɤɭ I2.
ɋ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɧɚɣɞɢɬɟ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ Ⱦɨɯɨɞɧɨɫɬɶ
ɩɨɪɬɮɟɥɹ (ɰɟɥɟɜɚɹ ɹɱɟɣɤɚ $C$6) ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɨɝɪɚɧɢɱɟɧɢɹɯ:
a) ɋɭɦɦɚ ɞɨɥɟɣ ɚɤɬɢɜɨɜ ɪɚɜɧɚ 1.
b) Ⱦɨɥɢ ɚɤɬɢɜɨɜ – ɧɟɨɬɪɢɰɚɬɟɥɶɧɵɟ ɱɢɫɥɚ.
c) Ɋɢɫɤ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɹ, ɡɚɞɚɧɧɨɝɨ ɜ ɹɱɟɣɤɟ I2.
ɋɨɯɪɚɧɢɬɟ ɢ ɩɪɨɚɧɚɥɢɡɢɪɭɣɬɟ ɧɚɣɞɟɧɧɨɟ ɪɟɲɟɧɢɟ.
Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ
ȿɫɥɢ ɩɨɪɬɮɟɥɶ ɧɚɫɱɢɬɵɜɚɟɬ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɛɭɦɚɝ, ɬɨ ɜ ɪɚɦɤɚɯ ɩɪɟɞɫɬɚɜɥɟɧɧɨɝɨ ɜɵɲɟ
ɚɥɝɨɪɢɬɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɟ ɨɱɟɧɶ ɭɞɨɛɧɨ ɜɜɨɞɢɬɶ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɞɢɫɩɟɪɫɢɢ ɞɨɯɨɞɚ.
Ɉɞɧɚɤɨ ɷɬɭ ɩɪɨɛɥɟɦɭ ɥɟɝɤɨ ɫɧɹɬɶ, ɟɫɥɢ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɦɚɬɪɢɱɧɵɦ ɢɫɱɢɫɥɟɧɢɟɦ.
Ɂɚɞɚɱɚ 3
Ɋɟɲɢɬɟ ɡɚɞɚɱɭ 2, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɦɚɬɪɢɱɧɵɦɢ ɮɭɧɤɰɢɹɦɢ ɞɥɹ ɪɚɫɱɟɬɚ ɞɢɫɩɟɪɫɢɢ ɞɨɯɨɞɚ.
ɉɊɂɆȿɑȺɇɂȿ:
1. ȼ ɹɱɟɣɤɚɯ ɋ10:ȿ10 ɪɚɡɦɟɫɬɢɬɟ ɬɪɚɧɫɩɨɧɢɪɨɜɚɧɧɭɸ ɦɚɬɪɢɰɭ ɞɨɥɟɣ ɚɤɬɢɜɨɜ.
2. Ⱦɢɫɩɟɪɫɢɸ ɞɨɯɨɞɚ ɜɵɱɢɫɥɢɬɟ ɩɨ ɮɨɪɦɭɥɟ: =ɆɍɆɇɈɀ(ɆɍɆɇɈɀ(C10:E10;C2:E4);F2:F4).
Ɂɚɞɚɱɚ 4
Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɨɪɬɮɟɥɹ ɞɥɹ ɞɚɧɧɵɯ, ɭɤɚɡɚɧɧɵɯ ɧɚ ɪɢɫɭɧɤɟ 10.2, ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɞɨɥɢ ɚɤɬɢɜɨɜ ɧɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ
ɢ ɨɠɢɞɚɟɦɚɹ ɞɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɧɟ ɧɢɠɟ 0,21.
2