Consider the following linear programming problem: A shoe company is introducing

Question

Consider the following linear programming problem:

A shoe company is introducing a new line of running shoes.

The marketing division decides to promote the line in a particular city. The promotion will consist of newspaper, radio, and television ads.

Each newspaper ad will cost $120, each television ad will cost $370, and each radio ad will cost $210.

The company wants to spend at most half of their money on ads in newspapers. They also would like to have at least 10 of each type of ad.

The marketing division believes that each newspaper ad will reach 4,700 men and 3,700 women, each television ad will reach 7,600 men and 6,600 women, and each radio ad will reach 4,500 men and 5,500 women.

The promotion will be considered successful if it reaches at least 400,000 men and 200,000 women.
  
The Advertising Budget is Limited to $21,000

How should the company divide its money between the newspaper, television, and radio ads so as to reach the required number of Men and Women at the Minimum Cost?

Choose the appropriate objective and constraints from the list below:

Question 14 options:

1)

4700N + 7600T + 4500R <= 21000

2)

N,T,R >= 0

3)

3700N + 6600T + 5500R >= 21000

4)

120N + 370T + 210R <= 21000

5)

120N <= .5(120N + 370T + 210R)

6)

N < .5(N + T + R)

7)

N,T,R Integers

8)

3700N + 6600T + 5500R >= 200,000

9)

4700N + 7600T + 4500R >= 400,000

10)

N,T,R >= 10

11)

N + T + R >= 10

12)

Minimize Cost = 120N + 370T + 210R

13)

Max Exposure = 8400N + 14200T + 10000R

1)

4700N + 7600T + 4500R <= 21000

2)

N,T,R >= 0

3)

3700N + 6600T + 5500R >= 21000

4)

120N + 370T + 210R <= 21000

5)

120N <= .5(120N + 370T + 210R)

6)

N < .5(N + T + R)

7)

N,T,R Integers

8)

3700N + 6600T + 5500R >= 200,000

9)

4700N + 7600T + 4500R >= 400,000

10)

N,T,R >= 10

11)

N + T + R >= 10

12)

Minimize Cost = 120N + 370T + 210R

13)

Max Exposure = 8400N + 14200T + 10000R

Explanation / Answer

Let N be the no. of newspapers advertisement, T be the no. of television advertisement and R be Radio Advertisement

Minimize Cost = 120N + 370T + 210R

Maximize Exposure = 8400N + 14200T + 10000R

subject to follwing constraints

120N + 370T + 210R <= 21000 (Using information that advertisement budget is 21000 dollars max and cost of each mode of advertisement)

120N <= .5(120N + 370T + 210R) (Using information that Newspaper Advertisement expenditure will be atmost half of the total advertisement spending)

3700N + 6600T + 5500R >= 200,000 (Using reach of each mode of advertisement to number of women and women to be exposed to advertisement atleast)

4700N + 7600T + 4500R >= 400,000 (Using reach of each mode of advertisement to number of men and men to be exposed to advertisement atleast)

N,T,R >= 10 (Using information that atleast 10 of each advertisement should be done)

Minimize Cost = 120N + 370T + 210R

Maximize Exposure = 8400N + 14200T + 10000R

subject to follwing constraints

120N + 370T + 210R <= 21000 (Using information that advertisement budget is 21000 dollars max and cost of each mode of advertisement)

120N <= .5(120N + 370T + 210R) (Using information that Newspaper Advertisement expenditure will be atmost half of the total advertisement spending)

3700N + 6600T + 5500R >= 200,000 (Using reach of each mode of advertisement to number of women and women to be exposed to advertisement atleast)

4700N + 7600T + 4500R >= 400,000 (Using reach of each mode of advertisement to number of men and men to be exposed to advertisement atleast)

N,T,R >= 10 (Using information that atleast 10 of each advertisement should be done)

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.