📘 linear programming

1. **State the problem:** We want to determine how many chairs ($x$) and tables ($y$) to produce to maximize or minimize an objective (not specified, so we assume maximizing produc

1. **Problem Statement:** We want to minimize the total number of doctors employed by the hospital while meeting daily doctor requirements and ensuring no more than 100 doctors sta

1. **State the problem:** We want to solve the linear programming problem using the simplex method:

1. **State the problem:** A machinist has 6 units of metal and 28 hours of free time to make two models of decorative computer screens: Model I and Model II.

1. **State the problem:** A machinist has 6 units of metal and 28 hours of free time to make two models of decorative computer screens. Model I requires 2 units of metal and 7 hour

1. **State the problem:** A machinist has 6 units of metal and 28 hours of free time to make two models of decorative computer screens. Model I requires 2 units of metal and 7 hour

1. **State the problem:** Minimize the objective function $$z = 5x_1 + 4x_2$$

1. **State the problem:** Minimize the objective function $$z = 5x_1 + 4x_2$$

1. **State the problem:** A shop wants to buy Pens and Notebooks to maximize profit. - Each Pen costs 2 and yields a profit of 1.

1. **State the problem:** Farmer Anuar wants to decide how many acres of corn ($x$) and paddy ($y$) to plant to maximize total revenue.

1. **Problem Statement:** A cook wants to mix two foods to get at least 8 units of vitamin A and 10 units of vitamin C. Food I has 2 units/kg vitamin A and 1 unit/kg vitamin C.

1. **Problem Statement:** A cook wants to mix two foods to get at least 8 units of vitamin A and 10 units of vitamin C.

1. **Problem Statement:** A cook wants to mix Food I and Food II to get at least 8 units of vitamin A and 10 units of vitamin C.

1. نبدأ بقراءة التمرين الثالث (P3) الذي هو مسألة برمجة خطية بصيغة: $$\max z = -b x$$

1. **بيان المشكلة:** نريد حل البرنامج الخطي (P1):

1. المشكلة: جدول السمبلكس لا يظهر. 2. جدول السمبلكس هو أداة تُستخدم في البرمجة الخطية لحل مسائل تحسين الدوال الخطية.

1. **بيان المسألة:** نريد إيجاد حل للبرنامجين الخطيين (P1) و(P2) المعطيين بالشكل التالي:

1. **State the problem:** Maximize the objective function $$Z = 7x_1 + 14x_2$$ subject to the constraints: $$3x_1 + 2x_2 \leq 36$$

1. Muammo: Berilgan chiziqli dasturlash masalasining o‘zgaruvchilar sonini aniqlash. 2. Masala funksiyasi: $$F(x_1, x_2, x_3, x_4) = 4x_1 - 3x_2 - 5x_3 + 2x_4 \to \min$$

1. Berilgan chiziqli dasturlash masalasi quyidagicha: $$F(x_1, x_2, x_3, x_4) = 4x_1 - 3x_2 - 5x_3 + 2x_4 \to \max,$$

1. Masalani bayon qilish: Berilgan chiziqli dasturlash masalasi $$F(x_1, x_2, x_3, x_4) = 4x_1 - 3x_2 - 5x_3 + 2x_4 \to \max$$ va cheklovlar: $$\begin{cases}-2x_1 + 4x_2 + x_3 - x_