Can i get the conclusion for this below goal programing ??

Objective of the Project:

The objective of this report is to identify the three target audiences customers are trying to reach and with having advertising budget of $600,000.

Defining Goals:

Goal 1: Advertisement needs to be seen by at least 40 million high-income men (HIM)

Goal 2: Advertisement needs to be seen by at least 60 million low-income people (LIP)

Goal; 3: Advertisement needs to be seen by at least 35 million high-income women (HIW)

Defining the Decision Variable:

The advertising during the football games and soap operas will cover the target audience and it is viewed by many viewers. The table below indicates the number of viewers from the different categories that will be viewing these types of programming.

	HIM	LIP	HIW	COST
Football ad(per min)	7 million	10 million	5 million	$100,000
Soap opera ad (per min)	3 million	5 million	4 million	$60,000

Expressing the goals as equation:

Let X₁ as minutes of football ad

Let X₂ as minutes of soap opera ad

Goal 1- (HIM) 7x₁ +3x₂ 40

Goal 2- (LIP) 10x₁ +5x₂ 60

Goal 3 HIW 5x₁ +4x₂ 35

Ad Budget) 100 X₁ + 60 X ₂ ^<_-600

Defining the Goal Constraints and Calculations:

Formulating the problem as an Linear programing

HIM) 7x₁ +3x₂ 40

(LIP) 10x₁ +5x₂ 60

HIW 5x₁ +4x₂ 35

(Ad Budget) 100 X₁ + 60 X ₂ ^<_-600

X_1, X₂ 0

So now we have the above goals, in goal programming we must remove the in equalities and add the slag variables

So, for the soft constrains we added deviation variables

d^- i = represents the amount by which each goals target value is underachieved,

d+i = represents the amount by which each goals target value is overachieved.

by introducing the deviation variables on the LHS

HIM 7x₁ +3x₂ + d1 d+1 = 40

LIP 10x₁ +5x₂ + d2 d+2 = 60

HIW 5x₁ +4x₂ + d3 d+3 = 35

x₁, x₂, d1 , d+1 ,+ d2 , d+2 , d3, d+3 0

We dont want to go below 40 for HIM

We dont want to go below 60 for LIP

And not below 35 for HIW

So, we need to minimize d1 , d2,d3

Suppose each shortfall of 1,000,000 viewers from the goal translates to a cost of $200,000 for HIM, 100,000 for LIP and for HIW its $50,000

Then the objective function will be

Min Z = 200 d1 +100 d2,+50 d3

Excel Calculations:

Exposures of each ad media to various groups (input data)
	Football ads	Soap opera ads	Goal weight	Goal level
High-income men	7	3	1	1
High-income women	5	4	1.2	1
Low-income people	10	5		2
Cost/unit	$1,00,000	$60,000

Cost of ads
	Football ads	Soap opera ads	Total	<=	Budget
	500000	100000	600000		$6,00,000
Achievement of goals
	Total exposures	Under goals	Sum		Goals
High-income men	40	0	40	>=	40
High-income women	31.66666667	3.333333333	35	>=	35
Low-income people	58.33333333	1.666666667	60	>=	60
Deviation fromgoals
	Deviation
Dev from goal 1	0
Dev from goal 2	3.333333333
Dev from goal 3	1.666666667
Weighted goals of L1	4