A department store chain has up to $22,000 to spend on television advertising for a sale. All ads will be placed with one television station, where a 30-second ad costs$1,000 on daytime TV and is viewed by 14,000 potential customers, $2,000 on prime-time TV and is viewed by 24,000 potential customers, and $1,500 on late-nightTV and is viewed by 18,000 potential customers. The television station will not accept a total of more than 20 ads in all three time periods.How many ads should be placed in each time period in order to maximize the number of potential customers who will see the ads?? How many potential customers willsee the ads? (lgnore repeated viewings of the ad by the same potential customer.) Include an interpretation of any nonzero slack variables in the optimal solution.Select the correct choice below and fill in any answer boxes present in your choice.A. The maximum number of potential customers who see the ads isdaytime ads,prime-time ads, andlate-night ads are placed.people whenO B. There is no way to maximize the number of potential customersClick to select and enter your answer(s) and then click Check Answer.partremaining1Clear AllCheck Answer

Question
Asked Oct 9, 2019
67 views
A department store chain has up to $22,000 to spend on television advertising for a sale. All ads will be placed with one television station, where a 30-second ad costs
$1,000 on daytime TV and is viewed by 14,000 potential customers, $2,000 on prime-time TV and is viewed by 24,000 potential customers, and $1,500 on late-night
TV and is viewed by 18,000 potential customers. The television station will not accept a total of more than 20 ads in all three time periods.
How many ads should be placed in each time period in order to maximize the number of potential customers who will see the ads?? How many potential customers will
see the ads? (lgnore repeated viewings of the ad by the same potential customer.) Include an interpretation of any nonzero slack variables in the optimal solution.
Select the correct choice below and fill in any answer boxes present in your choice.
A. The maximum number of potential customers who see the ads is
daytime ads,
prime-time ads, and
late-night ads are placed.
people when
O B. There is no way to maximize the number of potential customers
Click to select and enter your answer(s) and then click Check Answer.
part
remaining
1
Clear All
Check Answer
help_outline

Image Transcriptionclose

A department store chain has up to $22,000 to spend on television advertising for a sale. All ads will be placed with one television station, where a 30-second ad costs $1,000 on daytime TV and is viewed by 14,000 potential customers, $2,000 on prime-time TV and is viewed by 24,000 potential customers, and $1,500 on late-night TV and is viewed by 18,000 potential customers. The television station will not accept a total of more than 20 ads in all three time periods. How many ads should be placed in each time period in order to maximize the number of potential customers who will see the ads?? How many potential customers will see the ads? (lgnore repeated viewings of the ad by the same potential customer.) Include an interpretation of any nonzero slack variables in the optimal solution. Select the correct choice below and fill in any answer boxes present in your choice. A. The maximum number of potential customers who see the ads is daytime ads, prime-time ads, and late-night ads are placed. people when O B. There is no way to maximize the number of potential customers Click to select and enter your answer(s) and then click Check Answer. part remaining 1 Clear All Check Answer

fullscreen
check_circle

Expert Answer

Step 1

Let the number of ads on daytime, prime time late night is x , y , z respectively.

Since the number of ads are 20 and the cost of ads cannot exceed $22000.

Therefore,

help_outline

Image Transcriptionclose

1000x +2000y 1500z 22000 The potential consumers are given by p 14000x 24000y 18000z

fullscreen
Step 2

The problem is

help_outline

Image Transcriptionclose

p 14000x 24000y +18000z 1000x 2000y 1500z s 22000 x, y,z 20

fullscreen
Step 3

Since use the slack variable s1 and s2 to make the problem ...

help_outline

Image Transcriptionclose

p 14000x 24000y +18000z +0.s, +0.s, x+yzs 20 1000x 2000y +1500z +s, 22000 x, y,z 20

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.