4 A farmer has 500 acres of available land and $100,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c).Profits and Constraints for CropsCornPotatoesCabbageTotalNumber of AcresX1$320X2$128X3$224500s $100,000Cost (per acre)Profit (per acre)$120$40$60=(a) Give the dual problem.Minimizew = 500y, + 100000y2y, + 320y2 2y, + 128y2 2y, + 224y2 2 60y, 2 0, y2 20subject to:12040with(Simplify your answers. Do not factor.)(b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 450 acres but capital increases to $105,000.The farmer's estimated profit is $(Type an integer or a decimal.)(c) Suppose the farmer has 550 acres of land but only $95,000. Find the optimum profit and the planting strategy that will produce this profit.Planting acres of potatoes,(Type integers or decimals.)acres of com, and acres of cabbage will produce an optimal profit of $ Need b) and c) please

Objective Functions and Constraints: Based on the given details, the objective…

Answered: A farmer has 500 acres of available…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
B 8,000 A 4,000 10,000 20,000 Disposable income Figure 1.2 2) Refer to Figure 1.2. The slope of the line between Points A and B is A) 0.4. C) 2.5. B) 1.2. D) indeterminate from this information. Consumption
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26. XYZ and Co has provided the following data seeking your advice on optimum investment strategy: Net return data (in paise) Investment made at the of selected investments Amount beginning of year available (Lakh) 1 95 80 70 60 70 2 75 65 60 50 40 3 70 45 50 40 90 60 40 40 30 30 Маximum Investment (Lakh) 40 50 60 60 The following additional information is also provided: (i) P, Q, R and S represent the selected investments. (ii) The company has decided to have four-year investment plan. (iii) The policy of the company is that amount invested in any year will remain so until the end of the fourth year. (iv) The values (paise) in the table represent net return on investment of 7 1 till the end of the planning horizon (for example, a rupee invested in investment P at the beginning of first year will grow to { 1.95 by the end of the fourth year, yielding a return of 95 paise). Using the above, determine the optimum investment strategy. (CA, November, 1996)
The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car's frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 36,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,700 hours of assembly time will be available next quarter. The profit contributions are $200…
The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car's frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 38,000 pounds of the high-alloy steel will be avallable next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,800 hours of assembly time will be available next quarter. The profit contributions are $200…
5. The manager of a fast-food restaurant featuring hamburgers is adding salads to the menu. If they choose to include a salad bar (i.e., the MAKE option), it will cost $14,000 in annual fixed costs for the leased equipment and added employee, and $1 per salad variable cost. If they choose to have pre-made salads (i.e., the BUY option), it will cost $3 per salad. The manager expects to sell 7,500 salads per year. What is the make or buy quantity (i.e., the breakeven point between making vs. buying)?

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