Log I. Transportation. The manager of a small private company must decide how to supply his three mills with wood cut from three logging sites he will be operating next month. He would like to minimize the total daily travel cost from the logging sites to the mills. He has gathered the following information. It costs him $1.50 per mile to run his trucks. The one way travel distances are as tabulated: Logging Site 1 2 3 Distance in miles between logging sites and mills Mill A Mill B Mill C 8 15 50 10 17 20 30 25 15
Each load requires a round-trip from mill to site and back. Each mill must have a continuous daily supply of wood to keep the various operations working efficiently. The minimum number of truckloads required daily for each mill is 25. Each logging site can produce, at a maximum, the following truckloads daily: site 1, 20 loads; site 2, 30 loads, and, site 3, 25 loads. Formulate the problem as a set of linear equations to determine how many loads should be shipped daily from each logging site to each mill. Let Xij be the number of loads per day shipped from site i to mill j.
II. Mill Log Purchase. The management of a small mill has requested your assistance in addressing a log procurement problem. The issue involves the letting of contracts for the mill log supply during the next two quarters. In the first quarter the estimated log consumption is seven million board feet and in the second quarter the mill will need at least eight million board feet. Discussions with their three primary log suppliers and the mill accounting staff have produced the following tabulated information: Price per Mbf Gypo 1 $43.00 Quarter 1 Gypo 2 $45.00 Gypo 3 $48.00 Gypo 1 $34.00 Quarter Gypo 2 2 $35.00 Gypo 3 $33.00
The upper limit on the total supply of logs procurable in either quarter is determined also: Gypo 1 6MM Gypo 2 7MM Gypo 3 5MM
Set up the linear program that will minimize the total purchase cost of logs while meeting mill raw material requirements.
III. Mill Log Purchase 2. You are a small mill operator and you are buying your logs camp-run from several gypo loggers at $200 per Mbf. A grade scale on several truck loads from each gypo shows the following:
UTILITY LOG 20 20 10 PERCENTAGE IN EACH GRADE NO 4 SAWLOG NO 3 SAWLOG 30 30 20 30 20 60 NO 2 SAWLOG 20 30 10
GYPO
1 2 3
The current market price on these grades is known to be:
LOG GRADE PRICE/MBF UTILITY LOG $50 NO 4 SAWLOG $162 NO 3 SAWLOG $200 NO 2 SAWLOG $234
You need 150Mbf per day to feed your mill. Your after milling profit or loss on each of the grades is:
LOG GRADE PROFIT OR LOSS/MBF UTILITY LOG -$150 NO 4 SAWLOG -$50 NO 3 SAWLOG +$50 NO 2 SAWLOG +$80
You have two allocation alternatives with the logs ...