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Fungsi Tujuan: Meminimumkan
C=3×1+4×2

{:[" Fungsi Batasan : 1). "2X1+X2 >= 6.000],[" 2). "X1+3×2 >= 9.000],[X1 >= 0","X2 >= 0]:}

$1$ . Fungsi Tujuan: Meminimumkan $C=3 \times 1+4 \times 2$ $\newline$ $\begin{array}{r} \text { Fungsi Batasan : 1). } 2 X 1+X 2 \geq 6.000 \\ \text { 2). } X 1+3 \times 2 \geq 9.000 \\ X 1 \geq 0, X 2 \geq 0 \end{array}$

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Solve quadratic equations: word problems

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Q.

1

. Fungsi Tujuan: Meminimumkan

C=3 \times 1+4 \times 2

\newline

\begin{array}{r} \text { Fungsi Batasan : 1). } 2 X 1+X 2 \geq 6.000 \\ \text { 2). } X 1+3 \times 2 \geq 9.000 \\ X 1 \geq 0, X 2 \geq 0 \end{array}

Identify Objective Function: Identify the objective function and constraints. $\newline$ Objective function: $C = 3x_1 + 4x_2$ $\newline$ Constraints: $\newline$ $1$ ) $2x_1 + x_2 \geq 6$ $\newline$ $2$ ) $x_1 + 3x_2 \geq 9$ $\newline$ $3$ ) $x_1 \geq 0$ $\newline$ $4$ ) $x_2 \geq 0$
Plot Constraints on Graph: Plot the constraints on a graph to find the feasible region. $\newline$ This step involves drawing lines for each constraint and shading the area that satisfies all constraints.
Find Intersection Points: Find the intersection points of the constraints. This involves solving the system of inequalities.
Calculate Intersection Point: Calculate the intersection point of $2x_1 + x_2 = 6$ and $x_1 + 3x_2 = 9$ . Solving the system of equations: $2x_1 + x_2 = 6\ldots(1)$ $x_1 + 3x_2 = 9\ldots(2)$ Multiply equation $(2)$ by $2$ to eliminate $x_1$ : $2x_1 + 6x_2 = 18\ldots(3)$ Subtract equation $(1)$ from equation $(3)$ : $x_1 + 3x_2 = 9$ $0$ $x_1 + 3x_2 = 9$ $1$ $x_1 + 3x_2 = 9$ $2$ Substitute $x_1 + 3x_2 = 9$ $3$ in equation $(1)$ : $x_1 + 3x_2 = 9$ $5$ $x_1 + 3x_2 = 9$ $6$ $x_1 + 3x_2 = 9$ $7$ $x_1 + 3x_2 = 9$ $8$ $x_1 + 3x_2 = 9$ $9$ Check for math errors.

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