Question

A committee in charge of promoting a Ladies Professional Golf Association tournament is trying to determine how best to advertise the event during the two weeks prior to the tournament. The committee obtained the following information about the three advertising media they are considering using.

Category	Audience Reached per Advertisement	Cost per Advertisement	Maximum Numer of Advertisement
TV	200,000	$2,500	10
Radio	50,000	$400	15
Internet	100,000	$500	18

The last column in this table shows the maximum number of advertisements that can be run during the next two weeks; these values should be treated as constraints. The committee established the following goals for the campaign.

Priority Level 1 Goal

Goal 1: Reach at least 3.7 million people.

Priority Level 2 Goal

Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements.

Priority Level 3 Goal

Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements.

Priority Level 4 Goal

Goal 4: Limit the total amount spent for advertising to $20,000.

(a)

Formulate a goal programming model for this problem. (Let x₁ = number of TV advertisements, x₂ = number of radio advertisements, x₃ = number of internet advertisements, let d_{p i} be the deviation variable which is greater than the value of goal i, and let d_{n i} be the deviation variable which is less than the value of goal i, for i = 1, 2, 3, 4.)

Min P₁ (Need answer here) + P_{2 (need answer here)} + P_{3(need answer here)} + P_{4 (need answer here)}

s.t.

TV limit (need answer here)

Radio limit (need answer here)

Internet limit (need answer here)

Goal 1 (need answer here)

Goal 2 (need answer here)

Goal 3 (need answer here)

Goal 4 (need answer here)

x_i, d_{p j}, d_{n j} ≥ 0 for i = 1, 2, 3, and j = 1, 2, 3, 4

(b)

Use the goal programming computer procedure to solve the model formulated in part (a). (Round your answers down to the nearest integer.)

Category	Number of Advertisements
TV
Radio
Internet

Answer 1

Since the point of notice is to augment the contact greatest crowd

So the target work is

Max Z = 200,000x1+50,000x2+100,000x3

Subject to

2500x1+400x2+500x3 <=20000 (Cost requirement)

x1>=0.3(x1+x2+x3) TV :(Atleast 30% advertisement in television)

I.e 0.7x1-x2-x3>=0

x2<=0.2(x1+x2+x3)

For example - 0.2x1+0.8x2-0.2x3<=0 ( radio ad)

x1,x2,x3>=0, Non antagonism compel

The dominate answer for this issue is given underneath