Cinnamon Trails Golf Club has a national reputation for being innovative in providing low cost golf equipment to its clientele. One way they accomplish this is by reselling “experienced” golf balls – golf balls that have been ‘lost’ in lakes and ponds and ‘salvaged’ by professional golf ball rescuers at courses around Oklahoma.
Cinnamon Trails uses four golf ball salvage companies to stock their experienced ball selection. They buy golf balls from these companies in lot sizes of 30. The RW Company charges Cinnamon Trails $12 per lot, The Eastman Company charges $9.60 per lot, Mosier LTD. charges $13.20 per lot, and Dooley’s Divers charge $15.60 per lot.
For the next planning period, Cinnamon Trails wishes to buy between 50 and 75 lots (inclusive of the end points) of experienced golf balls. Contractually, Cinnamon Trails must buy at least 10% of total golf balls purchased (in lots) from (individually) the Eastman Company, Mosier LTD, and Dooley’s Divers. Cinnamon Trails does not have such an agreement with the RW Company.
Cinnamon Trails classifies the golf balls they receive from each company into one of four categories – Type I (excellent-condition name-brand balls like Nike, etc.), Type II (excellent condition lesser balls like Top Flight, etc.), Ugly balls (balls that look like they came from a lake), and “Throw-away” balls, golf balls that are in really bad shape and will only be used on the driving range. Historically, each company has provided the following percentage of the four golf ball types in their lots:
Company RW Eastman Mosier Dooley Retail Price
Type I 0.2 0.1 0.25 0.25 $1.00
Type II 0.6 0.6 0.45 0.45 $0.75
Ugly 0.1 0.1 0.15 0.1 $0.25
Throw 0.1 0.2 0.15 0.2 Range
Thus, using this historical data as representative of future composition of lots, we can assume that 10% (0.1) of the golf balls purchased from RW are Throw-away balls, 10% (0.1) are Ugly, 60% (0.6) are Type II, and 20% (0.2) are Type I. Likewise, for the other three companies. The retail price that  Cinnamon Trails charges per ball is also shown (in case that is relevant below).
a) Create an LP model that minimizes cost in purchasing golf balls from the four companies. Use lots as your units. Consider the constraints listed above in the third paragraph, PLUS your solution should provide:
- At least 46.75 usable lots of golf balls (non-Throw-Away golf balls) THIS IS NOT A
PERCENTAGE
- At least 20% of all golf balls purchased should be Type I balls.
- No greater than 27.5% of all golf balls purchased should be Ugly AND Throw-away
COMBINED.
Both of the last two constraints can also be measured/constructed with LOTS as the units.
b) What would change in our model if Cinnamon Trails wanted to maximize profit/return (sales price less cost)? Describe/show explicitly these changes in the model.

• As written, with following additions and clarifications.
• Data: Lot consistency measure – RW (6.75), Eastman(8), Mosier (7), Dooley (7.6).
• Part a) Find least cost solution to meet all requirements as written PLUS – Average lot consistency measure for purchased lots of golf balls must be greater than or equal to 7.25.
• Part b) Find the maximum profit solution (Ball sale price less cost to purchase) with all requirements as written and the same Weighted average lot consistency measure as above.
• Keep in mind that there are 30 balls per lot – each lot from each seller will have a certain ‘sales price’ based on typical composition of lots.
• In both part a and part b, add integer requirements for lots. Do this at the very end of your model building process solve on excel

Answer rating: 100% (QA)

a Linear Programming Model to Minimize Cost Lets denote the number of lots purchased from each compa... View the full answer