To solve this linear programming (LP) problem, we will define variables, an objective function, and constraints based on the given information.

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Variables

Let:

• $x$: the number of grams of Memo+ consumed.
• $y$: the number of grams of Omega consumed.

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Objective Function

The cost of Memo+ is 20 cents per gram, and the cost of Omega is 30 cents per gram. The objective is to minimize the total cost:
$\text{Minimize } C = 20x + 30y$

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Constraints

The constraints ensure that Rashid meets the minimum requirements for each nutrient.

1. SSS Requirement (at least 60 mg):
   Each gram of Memo+ provides 20 mg of SSS, and each gram of Omega provides 30 mg of SSS.
   $20x + 30y \geq 60$

2. BBB Requirement (at least 1000 mg):
   Each gram of Memo+ provides 500 mg of BBB, and each gram of Omega provides 250 mg of BBB.
   $500x + 250y \geq 1000$

3. GGG Requirement (at least 18 mg):
   Each gram of Memo+ provides 9 mg of GGG, and each gram of Omega provides 2 mg of GGG.
   $9x + 2y \geq 18$

4. HHH Requirement (at least 20 mg):
   Each gram of Memo+ provides 2 mg of HHH, and each gram of Omega provides 10 mg of HHH.
   $2x + 10y \geq 20$

5. LLL Requirement (at least 360 mg):
   Each gram of Memo+ provides 60 mg of LLL, and each gram of Omega provides 90 mg of LLL.
   $60x + 90y \geq 360$

6. Non-Negativity Constraints:
   Since Rashid cannot consume a negative quantity of supplements:
   $x \geq 0, \quad y \geq 0$

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Final LP Model

The complete linear programming problem is:
Minimize
$C = 20x + 30y$
Subject to

& 20x + 30y \geq 60 \quad \text{(SSS constraint)} \\ & 500x + 250y \geq 1000 \quad \text{(BBB constraint)} \\ & 9x + 2y \geq 18 \quad \text{(GGG constraint)} \\ & 2x + 10y \geq 20 \quad \text{(HHH constraint)} \\ & 60x + 90y \geq 360 \quad \text{(LLL constraint)} \\ & x \geq 0, \, y \geq 0 \quad \text{(Non-negativity constraints)} \end{aligned}$$ Would you like to see how this can be solved graphically or using another method? --- ### Related Questions: 1. How do we graphically represent the constraints to find the feasible region? 2. Can you explain the role of slack variables in LP problems? 3. How can we use simplex method to solve this LP problem? 4. What happens if the cost per gram of Memo+ changes? 5. How do sensitivity analyses apply to this scenario? --- ### Tip: Always start by analyzing the constraints individually when solving LP problems, ensuring you fully understand the feasible region before applying optimization techniques.