Operation Reaserch

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The Ploughman family farm owns and operates a 640-acre farm that has been in the family for several generations. The Ploughman always have had to work hard to make a decent living from the farm and have had to endure some occasional difficult years. Stories about earlier generations overcoming hardships due to droughts, floods, etc., are an important part of the family history. However, the Ploughman enjoy their self-reliant lifestyle and gain considerable satisfaction from continuing the family tradition of successfully living off the land during an era when many family farms are being abandoned or taken over by large agricultural corporations. John Ploughman is the current manager of the farm while his wife Eunice runs the house and…show more content…
(b) Formulate this model. (c) Obtain an optimal solution and generate the additional output provided for post-optimality analysis (e.g., the Sensitivity Report). What does the model predict regarding the family monetary worth at the end of the coming year? (d) Find the allowable range to stay optimal for the net value per acre planted for each of the three crops. The above estimates of the net value per acre planted in each of the three crops assume good weather conditions. Adverse weather conditions would harm the crops and greatly reduce the resulting value. The scenarios particularly feared by the family are a drought, a flood, an early frost, both a drought and an early frost, and both a flood and an early frost. The estimated net values for the year under these scenarios are as follows: Net Value per Acre Planted Net Value per Acre Planted Net Value per Acre Planted Scenario Soybeans Corn Wheat Drought -$10 -$15 $0 Flood $15 $20 $10 Early frost $50 $40 $30 Drought and early frost -$15 -$20 -$10 Flood and early frost $10 $10 $5 (e) Find an optimal solution under each scenario after making the necessary adjustments to the linear programming model formulated in part (b). In each case, what is the prediction regarding the family monetary worth at the end of the year? (f) For the optimal solution obtained under each of the six scenarios [including the good weather scenario considered in parts (a) and (d)], calculate

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