1. **State the problem:** We want to determine how many necklaces and bracelets to make to maximize profit, given constraints on gold, platinum, and demand. 2. **Define variables:** Let $x$ = number of necklaces Let $y$ = number of bracelets 3. **Write the objective function:** Maximize profit $P = 300x + 400y$ 4. **Write the constraints:** - Gold constraint: each necklace uses 3 ounces, each bracelet 2 ounces, total gold available is 18 ounces $$3x + 2y \leq 18$$ - Platinum constraint: each necklace uses 2 ounces, each bracelet 4 ounces, total platinum available is 20 ounces $$2x + 4y \leq 20$$ - Demand constraint for bracelets: no more than 4 bracelets $$y \leq 4$$ - Non-negativity constraints: $$x \geq 0, \quad y \geq 0$$ 5. **Summary:** The linear programming model is: $$\text{Maximize } P = 300x + 400y$$ subject to $$3x + 2y \leq 18$$ $$2x + 4y \leq 20$$ $$y \leq 4$$ $$x \geq 0, y \geq 0$$ This model can be solved using graphical or simplex methods to find the optimal number of necklaces and bracelets to maximize profit.