Case 5-3 in Hillier and Hiller Math 201 Project 1 Case 5-3 in Hillier and Hiller

Project 1 Final report due at start of class Thursday, October 23, 2008. Final reports submitted on Thursday after the start of class will accrue a 10% lateness penalty. No final reports will be accepted after Thursday, Oct. 23, 2008 for any reason, no matter how good the reason is. Final reports must be submitted in hard copy form; no email submissions will be accepted. Team leaders are responsible for collecting team contributions and compiling the final report. Go to www.calvin.edu/~cgm3/math201.html for downloadable materials.

Farm Management Problem John Ploughman Eunice Ploughman Grandpa Frank Phyllis Carl

Elements of the Problem Data Decisions Constraints Measure of Performance

Project 1 Data Family labor: home farm Wages from work on neighboring farm Season Hours Available Winter/Spring 4000 Summer/Fall 4500 Season Wages Winter/Spring $5/hr Summer/Fall $5.50/hr

Data, cont’d Two types of livestock: Three crops Dairy cows Chickens Soybeans (cash crop) Corn (cash crop and cattle feed) Wheat (cash crop and chicken feed)

Data, cont’d Livestock value: 30 cows, total value $35,000 2,000 hens, total value $5,000 $20,000 investment fund available to buy new livestock Each new cow: $1,500 Each new hen: $3 Barn can hold maximum of 42 cows Chicken house can hold maximum of 5,000 hens Depreciation: Value of herd of cows depreciates 10%/year Value of flock of hens depreciates 25%/year

Data, cont’d Available acreage for planting: 640 acres Total family living expenses: $40,000 / year

Person-hours required each month Data, cont’d Cow Hen Person-hours required each month 10 0.05 Grazing land required 2 acres Net annual cash income $850 $4.25

Data, cont’d Data per acre planted (estimates for good weather) W&S = Winter and Spring; S&F = Summer and Fall Soybeans Corn Wheat W&S Person-Hours 1.0 0.9 0.6 S&F Person-Hours 1.4 1.2 0.7 Net Value $70 $60 $40

Where do we want to end up? The family wants to decide how many acres to plant for each crop, and how many new livestock (cows and hens) to buy, with the goal of maximizing the family’s total monetary worth at the end of the coming year. As their consultants, we need to provide them with optimal solutions with respect to estimated conditions for good weather and bad weather (drought, flood).

Decisions How much acreage should be planted for each crop? How many new cows and hens should the family purchase?

Constraints The family needs to plant enough acres of corn to provide feed for the cows: Acres of corn > (1 acre/cow) times (# of cows) The family needs to plant enough acres of wheat to provide chicken feed: Acres of wheat > (0.05 acres/chicken) times (# of chickens) The total spent on new livestock must be no greater than the amount in the investment fund ($20,000) Barn constraint: total # of cows < 42 Chicken house constraint: total # of hens < 5,000

Constraints, cont’d Total hours worked by family = planting hours + livestock care hours + hours on neighboring farm Planting hours and livestock care hours determined by acreage and number of livestock Hours on neighboring farm: optional (decision) Total hours worked by family W&S must not exceed the total available (4,000 hrs) Total hours worked by family S&F must not exceed the total available (4,500 hrs)

Decisions, revised How much acreage should be planted for each crop? How many new cows and hens should the family purchase? How many hours should the family work on the neighboring farm?

Measure of Performance The measure of performance is the family’s total monetary worth at the end of one year. Their total monetary worth is the following sum: Total Net Income + End of Year Value of Assets + Leftover Investment Fund - Total Living Expense = Total Monetary Worth

Project Assignment Do parts a) – e) and g) – i) of Case 5-3, pp.182-183 in the textbook. Use the spreadsheet template provided on your instructor’s website to start your work. Hint for part d): the Sensitivity Report prints “objective coefficients” for functions that are not the final objective function. For example, the total net value of the plantings is a SUMPRODUCT of the acres planted cells and the net value cells. The Sensitivity Report treats the net value cells as “objective coefficients.” Thus, your assignment in part d) is to use the Sensitivity Report “objective coefficient” information to find allowable ranges for the net value per acre planted for each of the three crops.

Project Assignment Hint for part d) continued: a portion of the Sensitivity Report for the spreadsheet model: This is NOT the whole Sensitivity Report, just the portion relevant to part d).

Project Assignment Your report should model each scenario in part e) with its own spreadsheet model. These should be tabs in your Excel spreadsheet file. Planning: your study group should have at least parts a) - d) completed by Monday and have a very good start on parts e) – i). We will use lab time on Monday to help you complete the project, but you must come to lab with some work done already, or it will be difficult for me to help you.