Posted: September 16th, 2017

Tillman Chemicals, Inc. has five production facilities, labelled A through E, that provide chemicals and

Tillman Chemicals, Inc. has five production facilities, labelled A through E, that provide chemicals to five different regions, labelled 1 through 5. The production and shipping costs related to satisfying regional demand are listed in the following table:

Demand Regions A B C D E Demand
(Tankers/yr)
1 1885 4084 6283 3770 6911 810
2 3770 4398 6597 2513 7225 570
3 4084 1885 4398 4398 4084 600
4 6283 4398 9425 6597 3142 360
5 5341 4084 2827 6597 2513 300
Capacity (Tankers/yr) 555 1425 150 600 240
Prod. Costs per Tanker 31400 23500 52600 23000 29000

Tillman needs a production plan for the coming fiscal year. Answer the following questions:

1) If plants can produce however much they want to (infinite production capacity), how much should each plant produce, and what is the cost?
2) If plants can produce as much as they want to UP TO THEIR STATED CAPCITY, how much should each plant produce, and what is the cost?
3) If plants MUST produce at no less than 45% capacity, then what should each plant produce, and what is the cost?
4) What do you observe about the relationship between constraints in your model and cost?

Exercise #2

Your company is choosing among several locations for its offices, each of which must serve multiple U.S. states. Your high-end products require regular servicing by repair technicians, who must report to the appropriate sales office. There are four potential sales office sites under consideration: San Diego, Dallas, Kansas City, and Seattle. The annual fixed cost of the San Diego office is $173,500, Dallas is $129,200, Kansas City is $142,000, and Seattle is $147,500. Repair technicians must make repair trips out of these offices, with costs per trip described in the following table:

Travel Costs
State San Diego Dallas Kansas City Seattle # of Trips
Washington 225 325 275 100 40
Oregon 225 325 275 150 35
California 150 275 200 200 100
Idaho 225 275 200 200 25
Nevada 175 275 200 225 40
Montana 250 250 200 200 25
Wyoming 225 250 175 225 50
Utah 225 225 175 275 30
Arizona 150 275 175 325 50
New Mexico 200 200 150 375 40
N. Dakota 375 275 225 275 30
S. Dakota 375 250 200 275 20
Nebraska 325 175 200 325 30
Kansas 325 150 150 375 40
Oklahoma 325 100 200 375 55
Colorado 225 225 175 325 65
Each technician may make up to 25 repair calls each year. Answer the following:
Assuming that, at most, 10 technicians are allowed at any one office, where should the offices be, and how many technicians should be at each office?
Now assume that unlimited technicians are allowed at each office. Where should the offices be, and how many technicians should be at each office?
How confident are you that the answer for #2 represents the best possible solutions? Explain your answer, and, if appropriate, suggest what might constitute a better solution.

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