Answer to Question #208507 in Macroeconomics for ezu3136

Question

a firm plans to purchase at list 200 quintals of scrap containing high metal quality metal x and low quality metal y.

Answer 1

The complete question is:

A firm plans to purchase at least 200 quintals of scarp containing high-quality metal X and low-quality metal Y.It decides that the scrap to be purchased must contain at least 100 quintals of X-metal and not more than 35 quintals of Y – metal. The firm can purchase the scrap from two suppliers (A and B) in unlimited quantities. The percentage of X and Y metals in terms of weight in the scraps supplied by a and B is given below

The price of A’s scrap is 200 per quintal and that of B’s $ 400 per quintal. Formulate this problem as an LP model to determine the quantities that the firm should bury from the two supplies so as to minimize total purchase cost.

Solution

Variables

$x_1$ : Quantity of scrap which is bought from supplier A.

$x_2$ : Quantity of scrap which is bought from supplier B.

Objective function

$min \space 200x_ 1 +400x_ 2$

Constraints

$x_ 1 +x_ 2 ≥200$ (High-quality metal X)

$0.10x_ 1 +0.20x_ 2 ≤ 35$  (Low-quality metal Y)

 Non-negativity condition

$x_ 1 ,x _2 ≥0$