LVTV News The program manager for LVTV News would like to determine the best way
ID: 326586 • Letter: L
Question
LVTV News The program manager for LVTV News would like to determine the best way to allocate the time for the one hour evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 60-minute broadcast, 20 minutes are set aside for advertising. The station's broadcast policy states that at least 15% of the remaining time should be devoted to local news coverage; the time devoted to local news or national news must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment; the time devoted to the sports segment should be no longer than the total time spent on the local and national news; and at least 20% of the time should be devoted to the weather segment. The production costs per minute are $325 for local news, $300 for national news, $150 for weather, and $100 for sports. a. What is the minimum production cost that satisfies all constraints? b. According to the optimal solution, how any minutes are allocated to national news? c. How many minutes of local news could the program manager schedule and still have the same optimal solution? d. Interpret the shadow price for the constraint corresponding to the requirement that at least 15% of the available time should be devoted to local coverage. e. Interpret the shadow price for the constraint corresponding to the requirement that the time devoted to the local and the national news must be at least 50% of the total broadcast time.Explanation / Answer
Total broadcast time= 60 minutes
Less- Advertisment =20 minutes
Available time- 40 minutes
Local and National news should be 50% of broadcast time,= 30 minutes and local news should be atleast 15% of post ads time. Local news time-= 6 minutes and National news= 30-6=24 minutes
Remaining time= 40-30=10 minutes and each should be divided equally among sports and weather.
a-Minimum production cost= 6*325+24*300+5*150+5*100= $10400
b-24 minutes
c-6 minutes
d-shadow price = 6*325=$1950. It means that it cost more for sourcing local news
e- Shadow price= $9150.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.