Question

5. Define a linear programming objective and constraints that is applicable to Facebook. Provide the necessary calculations (graphically and algebraically)

Answer 1

Let’ say we will be increasing Facebook advertising budget, so, Objective function is Maximizing the Facebook advertising budget Z = 110*X1 + 180*X2

Here, X1 = Number of Entertainment Ad, X2 = Number of Educational Ad

Budget for each Entertainment Ad = 110 and Budget for each Educational Ad = 180,

Constraints are

120*X1+200*X2≤ 2500

125*X1+190*X2≤ 3000

Each Entertainment Ad can be sold at 120 and 125 and each Educational Ad can be sold at 200 and 190 for the above mentioned limit ,

adding the slack variable X3,
adding the slack variable X4, cause the constraints are having '≤'

first tableau

leaving variable is P3
entering variable is P2

Intermediate operations

Pivot row (Row 1):
2500 / 200 = 25 / 2
120 / 200 = 3 / 5
200 / 200 = 1
1 / 200 = 1 / 200
0 / 200 = 0

Row 2:
3000 - (190 * 25 / 2) = 625
125 - (190 * 3 / 5) = 11
190 - (190 * 1) = 0
0 - (190 * 1 / 200) = -19 / 20
1 - (190 * 0) = 1

Row Z:
0 - (-180 * 25 / 2) = 2250
-110 - (-180 * 3 / 5) = -2
-180 - (-180 * 1) = 0
0 - (-180 * 1 / 200) = 9 / 10
0 - (-180 * 0) = 0

leaving variable is P2
entering variable is P1

Intermediate operations

Pivot row (Row 1):
25 / 2 / 3 / 5 = 125 / 6
3 / 5 / 3 / 5 = 1
1 / 3 / 5 = 5 / 3
1 / 200 / 3 / 5 = 1 / 120
0 / 3 / 5 = 0

Row 2:
625 - (11 * 125 / 6) = 2375 / 6
11 - (11 * 1) = 0
0 - (11 * 5 / 3) = -55 / 3
-19 / 20 - (11 * 1 / 120) = -25 / 24
1 - (11 * 0) = 1

Row Z:
2250 - (-2 * 125 / 6) = 6875 / 3
-2 - (-2 * 1) = 0
0 - (-2 * 5 / 3) = 10 / 3
9 / 10 - (-2 * 1 / 120) = 11 / 12
0 - (-2 * 0) = 0

optimal solution value Z = 6875 / 3
X1 = 125 / 6
X2 = 0

Using Graphical Method: