A jewelry store makes necklaces and bracelets from gold and platinum. The store has developed the following linear programming model for determining the number of necklaces and bracelets (x1 and x2) to make in order to maximize profit:
Maximize Z = 300x1 + 400x2 1profit, $2
Subject to
3x1 + 2x2 ≤ 18 (gold, oz)
2x1 + 4x2 ≤ 20 (platinum, oz)
1x2 ≤ 4(demand, bracelets)
x1, x2 ≥ 0
a. Solve this model graphically.
b. The maximum demand for bracelets is 4. If the store produces the optimal number of bracelets and necklaces, will the maximum demand for bracelets be met? If not, by how much will it be missed?
c. What profit for a necklace would result in no bracelets being produced, and what would be the optimal solution for this problem?