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Temukan Solusi dan gambarkanlah grafik dari fungsi dibawah ini! F Tujuan: Memaksimumkan keuntungan Skincare 1.000 ×1+250 ×2 F Kendala: Batasan Produk Face Whitening : 0,50 ×1+0,25 ×2 <= 100 Batasan Produk Body Lotion: 0,25 ×1+X2 >= 100 X_(1) >= 0,X_(2) >= 0

Temukan Solusi dan gambarkanlah grafik dari fungsi dibawah ini!\newlineF Tujuan: Memaksimumkan keuntungan Skincare 1.000×1+250×2 1.000 \times 1+250 \times 2 \newlineF Kendala: Batasan Produk Face Whitening : 0,50×1+0,25×2≤100 0,50 \times 1+0,25 \times 2 \leq 100 \newlineBatasan Produk Body Lotion: 0,25×1+X2≥100 0,25 \times 1+X 2 \geq 100 \newlineX1≥0,X2≥0 \mathrm{X}_{1} \geq 0, \mathrm{X}_{2} \geq 0

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Q. Temukan Solusi dan gambarkanlah grafik dari fungsi dibawah ini!\newlineF Tujuan: Memaksimumkan keuntungan Skincare 1.000×1+250×2 1.000 \times 1+250 \times 2 \newlineF Kendala: Batasan Produk Face Whitening : 0,50×1+0,25×2≤100 0,50 \times 1+0,25 \times 2 \leq 100 \newlineBatasan Produk Body Lotion: 0,25×1+X2≥100 0,25 \times 1+X 2 \geq 100 \newlineX1≥0,X2≥0 \mathrm{X}_{1} \geq 0, \mathrm{X}_{2} \geq 0
  1. Identify Objective Function: : Identify the objective function for profit maximization.\newlineObjective function: Profit=1000x1+250x2\text{Profit} = 1000x_1 + 250x_2
  2. Write Constraints: : Write down the constraints for the products.\newlineConstraint for Face Whitening: 0.50x1+0.25x2≤1000.50x_1 + 0.25x_2 \leq 100\newlineConstraint for Body Lotion: 0.25x1+x2≥1000.25x_1 + x_2 \geq 100\newlineNon-negativity constraints: x1≥0,x2≥0x_1 \geq 0, x_2 \geq 0
  3. Set Up Inequalities: : Set up the system of inequalities to represent the constraints.\newline0.50x1+0.25x2≤1000.50x_1 + 0.25x_2 \leq 100\newline0.25x1+x2≥1000.25x_1 + x_2 \geq 100\newlinex1≥0x_1 \geq 0\newlinex2≥0x_2 \geq 0
  4. Graph Inequalities: : Graph the inequalities on a coordinate plane.\newlinePlot the lines for each inequality and shade the feasible region.
  5. Find Corner Points: : Find the corner points of the feasible region by solving the system of equations formed by the intersection of the constraints.\newlineSolve for the intersection of 0.50x1+0.25x2=1000.50x_1 + 0.25x_2 = 100 and 0.25x1+x2=1000.25x_1 + x_2 = 100.

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