A jewelry store makes necklaces and bracelets from gold and platinum. The store has developed the following lin- ear programming model for determining the number of necklaces and bracelets (x, and x,) to make in order to maximize profit: Maximize Z = 300x, + 400x2 (profit, $) subject to 3x1 + 2x2 < 18 (gold, oz) 2x, + 4x2 s 20 (platinum, oz) x2 54 (demand, bracelets) X1, x2 2 () a. Solve this model graphically. b. The maximum demand for bracelets is 4. If the store produces the optimal number of bracelets and neck- laces, 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 op- timal solution for this problem?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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A jewelry store makes necklaces and bracelets from gold
and platinum. The store has developed the following lin-
ear programming model for determining the number of
necklaces and bracelets (x, and x,) to make in order to
maximize profit:
Maximize Z = 300x, + 400x2 (profit, $)
subject to
3x1 + 2x2 < 18 (gold, oz)
2x, + 4x2 s 20 (platinum, oz)
x2 54 (demand, bracelets)
X1, x2 2 ()
a. Solve this model graphically.
b. The maximum demand for bracelets is 4. If the store
produces the optimal number of bracelets and neck-
laces, 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 op-
timal solution for this problem?
Transcribed Image Text:A jewelry store makes necklaces and bracelets from gold and platinum. The store has developed the following lin- ear programming model for determining the number of necklaces and bracelets (x, and x,) to make in order to maximize profit: Maximize Z = 300x, + 400x2 (profit, $) subject to 3x1 + 2x2 < 18 (gold, oz) 2x, + 4x2 s 20 (platinum, oz) x2 54 (demand, bracelets) X1, x2 2 () a. Solve this model graphically. b. The maximum demand for bracelets is 4. If the store produces the optimal number of bracelets and neck- laces, 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 op- timal solution for this problem?
Expert Solution
Step 1

 Given,

Maximize profit=300x_{1}+400x_{2}

 

Subject to:

3x_{1}+2x_{2}\leq18 ​(gold, oz)

 

2x_{1}+4x_{2}\leq20 ​(platinum, oz)

 

x_{2}\leq4 ​(demand, bracelets)

 

x_{1} ,x_{2}\ge0

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