Linear Programming Assignment

Running Head: LINEAR PROGRAMMING ASSIGNNMENT
Linear Programming Assignment
Name of the Student
Name of the University
Author Note

1LINEAR PROGRAMMING ASSIGNNMENT
Answer 1
(a) The decision variables involved in this problem are black beads and orange beads.
(b) Let x1 be denoted as black beads and x2 be denoted as orange beads. The objective
function can be given as:
Minimize Z=1.50 x1+ x2
Subject ¿ the constraints :
2 x1 + x2 ≥ 12
2 x1 + x2 ≤ 24
x1 ≥ 5
Again, the length of the beads cannot be negative. Hence the non-negativity constraints:
x1 ≥ 0 , x2 ≥ 0
(c) The LPP can be solved by graphical method in the following method:
Let L1: 2 x1 + x2 = 12
Now, the origin, O: (0, 0) satisfies (2 * 0) + (1 * 0) = 0 < 12
Therefore, origin does not satisfy the inequality 2 x1 + x2 ≥ 12
Hence, 2 x1 + x2 ≥ 12 is satisfied by all points on L1 and on the non-origin side of L1
Let L2: 2 x1 + x2 = 24
Now, the origin, O: (0, 0) satisfies (2 * 0) + (1 * 0) = 0 < 24
Therefore, origin satisfies the inequality 2 x1 + x2 ≤ 24
Hence, 2 x1 + x2 ≤ 24 is satisfied by all points on L2 and on the origin side of L2
Let L3: x1 = 5
Now, the origin, O: (0, 0) satisfies (0) < 5

2LINEAR PROGRAMMING ASSIGNNMENT
Therefore, origin satisfies the inequality x1 ≤ 5
Hence, x1 ≥ 5 is satisfied by all points on L3 and on the non-origin side of L3
(d) The corner points obtained by drawing the constraints are given in the following table:
Corner Points Co-Ordinates
A (5, 2)
B (5, 14)
C (12, 0)
D (6, 0)
(e) The objective function assuming a minimal cost of MVR 24.00 has been drawn in blue in
the graph below: