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raketka [301]
2 years ago
13

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
Mathematics
2 answers:
Assoli18 [71]2 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]2 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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<u>To reduce this term to the lowest term:</u>

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$50\times\frac{3}{8}=\frac{150}{8}

Now, divide the numerator and denominator by the greatest common factor.

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So, divide numerator and denominator by 2.

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