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Case problems | Numerical analysis homework help

Problem 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 station’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.

 

Problem 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?

 

Problem 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 “Trail Mix” and “Subway Mix”.

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.

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