A Jewelry store makes necklaces and bracelets from gold and platinum. vThe store has 18 ounces of gold and 20 ounces of platinum. vEach necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. vThe demand for bracelets is no more than four. vA necklace earns $300 in profit and a bracelet $400. vThe store wants to determine the number of necklaces and bracelets to produce in order to maximize profit.

a. Formulate a linear programming model for this problem.b. Solve this model using graphical analysis.

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afsahsaleem afsahsaleem · Answer 1 · 2019-12-22T08:08:48+01:00

Answer:

maximum profit is$2400 when 4 necklace and 3 brackets are made.

Step-by-step explanation:

Total gold = 18 ounces

Total platinum = 20 ounces.

let X₁ represents the necklace and X₂ represents the bracelets.

maximize:

[tex]300x_{1} + 400x_{2}[/tex]

with constraints:

for gold:

[tex]3x_{1} + 2x_{2} \leq 18[/tex]---(1)

for platinum:

[tex]2x_{1} + 4x_{2} \leq 20[/tex]---(2)

The demand for bracelets is no more than four i.e.

[tex]x_{2}\leq 4[/tex]---(3)

[tex]x_{1},x_{2}\geq 0[/tex]