Question 1200944: QUESTION ONE
a) Elaborate the assumptions underlying linear programming model
b) Explain the steps that are taken during decision making process
QUESTION TWO
A firm is engaged in producing two products A and B, each unit of product A requires 2 kg of row material and 4 labour hours for processing, whereas each unit of product B requires 3 kg of row material and 3 hours of labour of the same type. Every week, the firm has an availability of 60 kg of row material and 96 labour hours. One unit of product A sold yields $ 40 and one unit of product B sold gives $35 as profit.
Required: Formulate this problem as a linear programming problem to determine as to how many units of each of the products should be produd
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!  .
Let number of units of A be x and that of B be y
Raw Material
Product A Raw material = 2kg
Product B raw material =3kg
Available Raw material 60 kg per week
Labour
Product A 4hours
Product B 3 hours
Total hours avaiable = 96
We can formulate two equations as follows
 When x = 0, y=20 (0,20) When y=0, x=30 (30,0)
 When x=0 y=32 (0,32) when y=0 x=24 (24,0)
Profit be z
z=40x+35y
The feasible area is the shaded portion.
The points are O (0,0) C(24,0), P(18,8) ,D (0,32)
z=40x+35y
At O z=0
At C , 24*40+35*0 =960
At P 40*18+35*8= 1000
At D 40*0 +32*35= 700
At P(18,8) we get maximum output
18 units of A and 8 units of B
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