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Fungsi Tujuan : Meminimumkan
C=3×1+4×2
Fungsi Batasan : 1).
2×1+X2 >= 6.000
2).
x1+3x2 >= 9.000

x1 >= 0,x2 >= 0

$1$ . Fungsi Tujuan : Meminimumkan $\mathrm{C}=3 \times 1+4 \times 2$ $\newline$ Fungsi Batasan : $1$ ). $2 \times 1+X 2 \geq 6.000$ $\newline$ $2$ ). $x 1+3 x 2 \geq 9.000$ $\newline$ $x 1 \geq 0, x 2 \geq 0$

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Scale drawings: word problems

Full solution

Q.

1

. Fungsi Tujuan : Meminimumkan

\mathrm{C}=3 \times 1+4 \times 2

\newline

Fungsi Batasan :

1

).

2 \times 1+X 2 \geq 6.000

\newline

2

).

x 1+3 x 2 \geq 9.000

\newline

x 1 \geq 0, x 2 \geq 0

Write Objective Function: First, let's write down the objective function and constraints properly. $\newline$ Objective Function: Minimize $C = 3x_1 + 4x_2$ $\newline$ Constraints: $\newline$ $1$ ) $2x_1 + x_2 \geq 6,000$ $\newline$ $2$ ) $x_1 + 3x_2 \geq 9,000$ $\newline$ $x_1 \geq 0$ , $x_2 \geq 0$
Set Up Inequalities: Now, let's set up the inequalities to find the feasible region. $\newline$ We have two inequalities: $\newline$ $2x_1 + x_2 \geq 6,000$ (Constraint $1$ ) $\newline$ $x_1 + 3x_2 \geq 9,000$ (Constraint $2$ )
Solve for $x_2$ : Let's solve the first inequality for $x_2$ to graph it. $\newline$ $x_2 \geq 6,000 - 2x_1$
Solve for $x_2$ : Now, let's solve the second inequality for $x_2$ to graph it. $\newline$ $x_2 \geq (9,000 - x_1) / 3$
Find Intersection Points: We can graph these inequalities on a coordinate plane, but since we're focusing on calculations, let's find the intersection points of the lines by setting the right sides of the inequalities equal to each other. $\newline$ $6,000 - 2x_1 = \frac{9,000 - x_1}{3}$
Multiply and Simplify: Multiply both sides by $3$ to get rid of the fraction. $3(6,000 - 2x_1) = 9,000 - x_1$
Add and Subtract: Simplify the equation. $\newline$ $18,000 - 6x1 = 9,000 - x1$
Simplify: Add $6x_1$ to both sides and subtract $9,000$ from both sides to solve for $x_1$ . $\newline$ $18,000 - 9,000 = 6x_1 - x_1$
Divide and Solve: Simplify the equation. $9,000 = 5x1$
Divide and Solve: Simplify the equation. $\newline$ $9,000 = 5x_1$ Divide both sides by $5$ to solve for $x_1$ . $\newline$ $x_1 = \frac{9,000}{5}$ $\newline$ $x_1 = 1,800$

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