CASE A

The program manager, Matt Simon, for TV Channel 25 would like to determine the best way to allocate the time for the 11:00-11:40 evening news broadcast. He would like to know the most profitable way to allocate broadcast time to local news, national news, weather, sports, and commercials. Over the forty-minute broadcast, no more than twelve minutes can be set aside for commercial advertising which generates the sole profit at a rate of $2750 per minute. The stationâ€™s broadcast policy states that at least 18% of the time available should be devoted to local news coverage; the time devoted to local news and national news combined must be at least 45% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to sports segment; the time devoted to the sports segment should be no longer than the combined time spent on the local and national news; and at least 15% of the broadcast time should be devoted to the weather segment. The production costs per minute are $450 for local news, $300 for national news, $220 for weather, and $170 for sports.

(

**A-1) Formulate and list a linear program model to help Mr. Matt Simon with his managerial problem at Channel 25.****(A-2) Use the software LINGO to solve your model and report the optimal broadcasting time allocation.**

**(A-3) Report the maximized profit.**

**CASE B**

A car dealership is offering the following three 2-year leasing options:

Plan I: Fixed Monthly Payment is $200 per month. Additional cost per mile is $0.095 per mile

Plan II: Fixed Monthly Payment is $300 per month. Additional cost per mile is $0.061 per mile for the first 6,000 miles. After that is $0.050 per mile.

Plan III: Fixed Monthly Payment is $170 per month. No additional cost per mile for the first 6,000 miles. After that is $0.14 per mile.

Assume a customer expects to drive between 15,000 to 35,000 miles during the next 2 years according to the following probability distribution:

Probability (Driving 15,000 miles) = 0.15

Probability (Driving 20,000 miles) = 0.20

Probability (Driving 25,000 miles) = 0.35

Probability (Driving 30,000 miles) = 0.15

Probability (Driving 35,000 miles) = 0.15

**(B-1) Construct a payoff matrix for this problem.**

**(B-2) Construct a regret table and report what decision should be**

**made according to the Minimax regret approach.**

**(B-3) What decision should be made according to the expected value**

**approach?**

**(B-4) What is the EVPI for this problem?**

**CASE C**
A small shop located in Utica sells a variety of dried fruits and nuts. The shop caters to travelers of all types; it sells one-pound boxes of individual items, such as dried bananas, as well as two kinds of one-pound boxes of mixed fruits and nuts, called â€œTrail Mixâ€ and â€œSubway Mixâ€.

Because of the health inspection issues, individual items and mixed items can only be sold as packaged one-pound boxes. Here are the amounts of current supplies:

Dried Bananas: 800 pounds

Dried Apricots: 600 pounds

Coconut Pieces: 500 pounds

Raisins: 700 pounds

Walnuts: 1200 pounds

The selling prices of the various types of boxes offered are:

Trail Mix: $9 per box

Subway Mix: $12 per box

Dried Bananas: $5 per box

Dried Apricots: $8 per box

Coconut Pieces: $10 per box

Raisins: $6 per box

Walnuts: $15 per box

The manager would like to obtain as much revenue as possible from selling these boxed products. The management also decided that no more than 70% but at least 30% of these boxed products should be allocated to the Mixes. The Trail Mix consists of equal parts of all individual items, whereas the Subway Mix consist of 2 parts of walnuts and one part each of dried bananas, raisins, and coconut pieces. There are no dried apricots in the Subway Mix.

**(C-1) Formulate and list the linear program model for this problem.**

**(C-2) Use the software LINGO to solve the model and report your production decision.**

**(C-3) Report the maximized revenue.**