Question

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

Answer 1

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)

Answer 2

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