1. Muammo: Eng kam xarajatlar usulida transport masalasining boshlang‘ich tayanch rejasini topish. 2. Formulalar va qoidalar: - Har bir manba (A_1, A_2, A_3) va har bir qabul qiluvchi (B_1, B_2, B_3, B_4) uchun mavjud bo‘lgan resurs va talablar berilgan. - Eng kam xarajatlar usuli: har doim eng kam xarajatli katakdan maksimal miqdorni ajratib, qolgan talab va taklifni yangilab borish. 3. Boshlang‘ich ma'lumotlar: - Xarajatlar matritsasi: $$\begin{bmatrix} 2 & 3 & 4 & 6 \\ 1 & 5 & 2 & 6 \\ 6 & 5 & 2 & 5 \end{bmatrix}$$ - Takliflar (A_1=4, A_2=2, A_3=3) - Talablar (B_1=3, B_2=2, B_3=2, B_4=2) 4. Hisoblash: - Eng kam xarajatli katakni topamiz: 1 (A_2, B_1) - A_2 taklifi 2, B_1 talabi 3, minimal 2 ni ajratamiz: $x_{2,1} = 2$ - Yangilangan taklif: A_2 = 0, talab: B_1 = 1 - Endi eng kam xarajatli kataklar qoldi: (A_1,B_1)=2, (A_1,B_2)=3, (A_1,B_3)=4, (A_1,B_4)=6, (A_3,B_1)=6, (A_3,B_2)=5, (A_3,B_3)=2, (A_3,B_4)=5 - Eng kam xarajatli katak: 2 (A_1,B_1) - A_1 taklifi 4, B_1 talabi 1, minimal 1 ni ajratamiz: $x_{1,1} = 1$ - Yangilangan taklif: A_1 = 3, talab: B_1 = 0 - Endi B_1 talabi qondirildi, B_2, B_3, B_4 talablariga qaraymiz. - Eng kam xarajatli katak: 2 (A_3,B_3) - A_3 taklifi 3, B_3 talabi 2, minimal 2 ni ajratamiz: $x_{3,3} = 2$ - Yangilangan taklif: A_3 = 1, talab: B_3 = 0 - Endi eng kam xarajatli kataklar: (A_1,B_2)=3, (A_1,B_3)=4, (A_1,B_4)=6, (A_3,B_2)=5, (A_3,B_4)=5 - Eng kam xarajatli katak: 3 (A_1,B_2) - A_1 taklifi 3, B_2 talabi 2, minimal 2 ni ajratamiz: $x_{1,2} = 2$ - Yangilangan taklif: A_1 = 1, talab: B_2 = 0 - Endi eng kam xarajatli kataklar: (A_1,B_3)=4, (A_1,B_4)=6, (A_3,B_2)=5, (A_3,B_4)=5 - Eng kam xarajatli katak: 4 (A_1,B_3) - A_1 taklifi 1, B_3 talabi 0, B_4 talabi 2, A_3 taklifi 1 - B_3 talabi 0, shuning uchun B_4 ga qaraymiz. - Eng kam xarajatli katak: 5 (A_3,B_4) - A_3 taklifi 1, B_4 talabi 2, minimal 1 ni ajratamiz: $x_{3,4} = 1$ - Yangilangan taklif: A_3 = 0, talab: B_4 = 1 - Endi faqat A_1 va B_4 qoldi: - $x_{1,4} = 1$ 5. Yakuniy boshlang‘ich tayanch reja matritsasi: $$\begin{bmatrix} 1 & 2 & 0 & 1 \\ 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 1 \end{bmatrix}$$ Bu matritsa barcha talab va taklifni qondiradi va eng kam xarajatlar usuliga mos keladi.