A potato farmer is studying the risks associated with planting his potato crop.

Question

A potato farmer is studying the risks associated with planting his potato crop. Based on past experience, he assesses the probabilities associated with potato prices per hundredweight (cwt), yields in cwt per acre, and costs (for fertilizer, water, seed, and labor) per acre (see table below). 5. Yield Probability (cwt per acre) Probability 210 220 230 240 250 Cost (per acre $400 500 600 Price (per cwt) $2 Probability 0.70 0.20 0.10 0.20 0.50 0.10 0.05 0.05 1.00 0.10 0.10 0.40 0.30 0.10 1.00 1.00 The profit per acre is (Price Yield) -Cost. Assume all probabilities are independent. Using expected value estimates, what are the average price, yield, cost and profit? Using the Monte Carlo method for 25 trials, (1) estimate the expected profit per acre and (2) the probability distribution per acre. (3) What is the probability that the farmer makes less than $100 per acre on his crop? a. b. c. Analyze and compare the results in 'a and 'b' above.

Explanation / Answer

Answer to Section (a)

Using Expected Values Estimates Formla, here are the average price, yield, cost and profit:

Average Profit Per Acre = (Average Price * Average Yield) - Average Cost

Average Profit = ( 3.95 X 232) - 440 = $ 476.40

Average Price Calculation Price (Per CWT) - A Probability - B Average Price - A X B $ 2.00 0.10 $ 0.20 $ 3.00 0.20 $ 0.60 $ 4.00 0.50 $ 2.00 $ 5.00 0.10 $ 0.50 $ 6.00 0.05 $ 0.30 $ 7.00 0.05 $ 0.35 Average Price Sum = $ 3.95 Per CWT

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.