Arec 525 agribusiness operations research methods assignment

Question

AREC 525 - Agribusiness Operations Research Methods Assignment- The University of Tennessee, Knoxville

Problem I

Tropicsun is a leading grower and distributor of fresh citrus products with three large citrus groves scattered around central Florida in the cities of Mt. Dora, Eustis, and Clermont. Tropicsun currently has 275,000 pounds (lbs) of citrus at the grove in Mt. Dora, 400,000 lbs at the grove in Eustis, and 300,000 lbs at the grove in Clermont. Tropicsun has citrus processing plants in Ocala, Orlando, and Leesburg with processing capacities to handle 200,000, 600,000, and 225,000 lbs, respectively. Tropicsun contracts with a local trucking company to transport its fruit from the groves to the processing plants. The trucking company charges a flat rate for every mile regardless of how many pounds of fruit are shipped. The following table summarizes the distances (in miles) between the groves and processing plants:

Table 1. Distance (in miles) between the groves and processing plants

	Processing Plant
Grove	Ocala	Orlando	Leesburg
Mt. Dora	21	50	40
Eustis	35	30	22
Clermont	55	20	25

Tropicsun wants to determine how many pounds to ship from each grove to each processing plant to minimize the total transportation cost. Please formulate an integer linear programming model for this problem. You need to define variables, notations, and subscripts clearly if you use the general form.

Problem II

Blue Ridge Hot Tubs manufactures and sells three models of hot tubs: Aqua-Spa, Hydro-Lux, and Typhoon-Lagoons. Each Aqua-Spa requires 1 unit of pump, 9 hours of labor, and 12 feet of tubing. Each Hydro-Lux requires 1 unit of pump, 6 hours of labor, and 16 feet of tubing. Each Typhoon-Lagoon requires 1 pump, 8 hours of labor, and 13 feet of tubing. The cost of acquiring a pump and a foot of tubing is $585 and $4.5, respectively, and the hourly labor cost is $22.5.

The company has 200 pumps, 1566 production labor hours, and 2880 feet of tubing available during the next production cycle. Also, the company's marketing research team estimates the demand function for each hot tube model as below:

Aqua-Spa: Q_Aqua = 300 - 0.175×P_Aqua
Hydro-Lux: Q_Hydro = 260 - 0.15×P_Hydro
Typhoon-Lagoons: Q_Typhoon = 245 - 0.16×P_Typhoon

The marketing team now reports that the prices for the similar products from the competing brands range between $1,000 and $1,500. The company intends to meet the demand and does not want to carry inventory. The company now consults you to determine the selling price of those three hot tub models (i.e., P_Aqua, P_Hydro, P_Typhoon) to maximize its profits.

A. Formulate the mathematical programming model for this problem.
B. Solve the model in a spreadsheet.
C. Interpret and summarize the results.
D. Which of the resource constraints are binding at the optimal solution? What is the shadow price of that binding constraint?
E. Due to the COVID-19 issue, the available labor hours for the next production cycle drop by 20%, what are the new optimal solution?

Problem III

Farmer Eric has a total of 2500 acres of land in which 1000 acres are in a very good quality of land (L1). The remaining 1500 acres of land are highly erodible with 1300 acres are classified as a medium quality (L2) and 200 acres as a poor quality (L3). The Natural Resources Conservation Service (NRCS) has indicated that the highly erodible lands cannot be used for low residue crops such as cotton or soybeans. However, the NRCS allows Eric to plant cotton and soybeans on the highly erodible land if he adopts no-till practices. Eric's experience shows that the production costs of no-till soybean and cotton will increase by 10% per acre. Also, no-till practices will reduce cotton yield by 15% but have no impact on soybean yield. The yield records of corn, cotton and soybeans for the three soils at Eric's farm can be found in Table 1. The production costs summary of those three crops is presented in Table 2. Eric also learns that one tractor will provide a maximum of 400 hours of time per month and costs $15/acre-hour to run. The months of April, May, and October will be critical to the farming operation. The estimated time for conventional tillage is summarized in Table 3. Also, he expects a 40% reduction in the tractor use time for cotton and soybeans in April and May if no-till practices are applied. The expected selling price at harvest are $0.85/pound for cotton, $5.80/bushel for corn, and $9.35/bushel for soybeans. Eric asks for your advice to determine what crops to plant, where to plant the crops, and the acreage of the planted crops to maximize his farming profit.

Table 1: Yield records on Eric’s farm

Land Quality	Cotton	Corn	Soybeans
	Pounds	Bushels
L1	1.6	145	42
L2	1.0	110	30
L3	0.9	95	28

Table 2: Cost records on Eric’s farm

Land Quality	Cotton - Conventional	Corn - Conventional	Soybeans - Conventional
	Dollars/acre
L1	320	220	150
L2	335	190	130
L3	285	175	135

Table 3: Hours of tractor use by critical month

Land Quality	Cotton- Conventional	Corn - Conventional	Soybeans - Conventional
	Hours/acre
April	2	2	1
May	7	5	3
October	5	2	2

a) Formulate an LP model for this problem.
b) Solve the model using the spreadsheet modeling.
c) Interpret and summarize the results.
d) If now corn prices drops to $4.05/bushel, what will be the optimal solution?

Problem IV

Mrs. Carol Ford approaches you for your advice to make an investment portfolio. She has paid attention to the four stocks, namely Stock C, Stock P, Stock M, and Stock V, and obtained the quarterly returns over the past five years (see the "Data.xlsx" file). She asks you to determine the percentage of her money to be allocated to each of the stocks.

A. Estimate the average annual returns and associated variance/covariance of those four stocks.

B. Suppose Mrs. Ford is completely risk averse. Determine the percentage allocated to each stock in her portfolio, and the resulting expected risk and return using Solver.

C. Now suppose Mrs. Ford is completely insensitive to risk and intends to maximize possible return. Determine the percentage allocated to each stock in her portfolio, and the resulting expected risk and return using Solver.

D. If Mrs. Ford wants to maximize the average returns on the stocks while minimizing the risk of her investment portfolio. Determine the solution that minimizes the maximum percentage deviation from the two optimal objectives using the MINIMAX method with Solver.

E. Derive an efficient frontier for the portfolio by assigning the respective weight to returns and risk, i.e. (W_returns, W_risk), as (10,1), (5,1), (2,1), (1,1), (1,2), (1,5) and (1,10) in part d.

F. Mrs. Ford is now particularly interested in the stock P and would like to get the forecasts of the returns in the next four quarters (i.e., 2019 Q1 - 2019 Q4) for this stock. Please use Holt's method and Solver to minimize the MSE between the actual and predicted stock returns. Determine the forecasted returns for the next four quarters using this technique.

G. Now use Holt-Winter's method for additive seasonal effects and Solver to minimize the MSE between the actual and predicted stock returns. Determine the forecasted returns for the next four quarters using this technique.

H. Which forecasting method will you recommend based on the results in parts f and g? Why?

Problem V

You are consulted by an owner of a local delivery service. He has three trucks to run the business. Now he is contracted to deliver 15 shipping boxes of produces to customers in 15 locations. The weight of each box is summarized in Table 1 and the load capacities of each truck is presented in Table 2.

Table 1: Weight of produces in each box

Box #	Box 1	Box 2	Box 3	Box 4	Box 5	Box 6	Box 7	Box 8
Weight (lbs)	80	95	125	210	160	320	90	110
Box #	Box 9	Box 10	Box 11	Box 12	Box 13	Box 14	Box 15
Weight (lbs)	70	210	260	170	240	80	180

Table 2: Load capacities of truck

Truck	Weight Capacity	Box Capacity	Cost per pound
1	800 pounds	5	$0.34
2	900 pounds	6	$0.42
3	850 pounds	5	$0.25

The owner would like to load each truck with five boxes and 800 pounds while minimizing the total shipping costs. There is an additional charge of $50 per box if trucks carrying extra boxes. Similarly, a charge of $0.10 per pound will be imposed for trucks carrying less weight.

Formulate the integer goal programming model for this problem. You need to define variables, notations, and subscripts clearly if you use the general form.

Format your assignment according to the give formatting requirements:

a. The answer must be double spaced, typed, using Times New Roman font (size 12), with one-inch margins on all sides.

b. The response also includes a cover page containing the title of the assignment, the course title, the student's name, and the date. The cover page is not included in the required page length.

c. Also include a reference page. The references and Citations should follow APA format. The reference page is not included in the required page length.