Question

A finished product must weigh exactly 150 grams. The raw materials
used in manufacturing the product are A, with a cost of Birr 2 per unit
and B with a cost of Birr 8 per unit. At least 14 units of B and not more
than 20 units of A must be used. Each unit of A and B weighs 5 and 10
grams respectively. How much of each type of raw materials should be
used for each unit of the final product in order to minimize the cost of
making the final product?
Required:
a. formulate the LPM for the problem
b. solve it using simplex method
c. interpret your result​

Answer 1

Given :  A finished product must weigh exactly 150 gram

The raw materials used in manufacturing the product are A

To Find : . formulate the LPP problem

minimize the cost

Solution:

B ≥ 14

A  ≤ 20

   5A + 10B  = 150

=>  A + 2B =  30

Cost C = 2A  + 8B

A = 10   B = 15

A = 2    B = 14

(0 , 15)  and ( 2 , 14)

C = 2A  + 8B

= 2(10) + 8(15)

= 20 + 120

= 140

C = 2(2) + 8(14)

= 4 + 112

= 116

Cost is 116  when  A = 2  and B = 14

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