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3 years ago

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Kings Department Store has 625 rubies, 800 diamonds, and 700 emeralds from which they will make bracelets and necklaces that the

y have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds. Kings will sell each bracelet for $400 and it costs them $150 to make it. Each bracelet is made with 2 rubies, 3 diamonds, and 4 emeralds. Kings will sell each necklace for $700 and it costs them $200 to make it. Each neckalce is made with 5 rubies, 7 diamonds, and 3 emeralds. a) Formulate the above problem as a Linear Programming problem with the objective of maximizing profit

2 answers:

Assoli18 [71]3 years ago

8 0

Step-by-step explanation:

Let Xb be the no of braclets made

Let Xn be the no of necklaces made

Max Z=250Xb + 500Xn (Objective Function)

Subject to

2Xb + 5Xn <= 625 (rubies)

3Xb + 7 Xn <= 800 ( diamonds)

4Xb + 3 Xn <= 700 (Emeralds)

Xb>=0 (non-negativity)

Xn >= 0 (non negativity

chubhunter [2.5K]3 years ago

4 0

Answer:

Step-by-step explanation:

We are to Formulate the question given as a Linear Programming problem with the objective of maximizing profit.

From the question;

Kings will sell each bracelet for $400 and it costs them $150 to make it.

This implies that; King will net a profit on $250 on each bracelet made with 2 rubies, 3 diamonds, and 4 emeralds :

Also;

Kings will sell each necklace for $700 and it costs them $200 to make it

i.e King will net a profit of $500 on each necklace made with 5 rubies, 7 diamonds, and 3 emeralds.

Now; let's assume that :

$Y_{br}$ be the no of bracelets made ; &

$Y_{nk}$ be the no of necklaces made

$\\ \\Max \ Z=250 \ Y{_b_r}} + 500 \ Y{_n_k}$ (Objective Function)

Subject to :

$2 \ Y_{br} + 5 \ Y_{nk}$ ← 625 (rubies)

$3 \ Y_{br} + 7 \ Y_{nk}$ ← 800 ( diamonds)

$4 \ Y_{br} + 3 \ Y_{nk}$ ← 700 (Emeralds)

$\\ \\Y_{br} \\$ ⇒ 0 (non-negativity)

$\\\\ \ Y_{nk}\\$ ⇒ 0 (non negativity)

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