Please show work using matrices, thank you! A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts a. through c.belowNumber of AcresCost (per acre)Profit (per acre)a. Give the quai propiem▼subject towithProfits and Constraints for CropsPotatoesCornX₂$128$40W=X1$320$120Y₁ + 320y₂Y₁ + 128y2Y₁ +224y₂Y₁ 20, y₂ 20₂12040▼60CabbageX3$224$60Total400$80,000b. 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 360 acres but capitalincreases to $84,000.The farmer's estimated profit is $c. Suppose the farmer has 440 acres of land but only $76,000. Find the optimum profit and the planting strategy that will produce this profit.Planting acres of potatoes,acres of com, andacres of cabbage will produce an optimal profit of $*

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

A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which 'maximizes his profit. Complete parts a. through c. below Number of Acres Cost (per acre) Profit (per acre) a. Give the quai propiem ▼ subject to Profits and Constraints for Crops Potatoes W= 21 $320 $120 Y₁ +320y2 Y₁ + 128y2 ₂ 120 40 Corn X₂ $128 $40 Cabbage X3 $224 $60 Total 400 $80,000 *

A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which 'maximizes his profit. Complete parts a. through c. below Number of Acres Cost (per acre) Profit (per acre) a. Give the quai propiem ▼ subject to Profits and Constraints for Crops Potatoes W= 21 $320 $120 Y₁ +320y2 Y₁ + 128y2 ₂ 120 40 Corn X₂ $128 $40 Cabbage X3 $224 $60 Total 400 $80,000 *

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-1. Which is more desirable assuming data are COST Decenaine the cousen dagram. 60 90 60 1/3 (45) 45 99 40 50 50 30 20 /2 40 50 B-2. A firm must decide whether to construct a small, medium or large stamping plant. A consultant's report indicates a 0.20 probability that demand will be low and 0.80 that demand will be high. If the firm builds a small facility and demand turns out to be low, the Net Present Value (NPV) will be $42M. If demand turns out to be high, the firm can either subcontract and realize the NPV of $42M or expand greatly for a Net Present Value of $48M. The firm could build a medium size facility as a hedge: if demand turns out to be low, its NPV is estimated at $22M; if demand turns out to be high, the firm could do nothing and realize a NPV of $46M, or could expand and realize a NPV of $50M. If the firm builds a large facility and demand is low, the NPV will be ($20M), whereas high demand will result in a NPV of $72M. a) Analyze and solve this problem using a…
A-1. Which is more desirable assuming data are PROFIT Decertaine the course dagram. 90 60 Va (45) 45 99 50 50 30 .20 /2 40 50 A-2. A firm must decide whether to construct a small, medium or large stamping plant. A consultant's report indicates a 0.20 probability that demand will be low and 0.80 that demand will be high. If the firm builds a smll facility and demand turns out to be low, the Net Present Value (NPV) will be $42M. If demand turns out to be high, the firm can either subcontract and realize the NPV of $42M or expand greatly for a Net Present Value of $48M. The firm could build a medium size facility as a hedge: if demand turns out to be low, its NPV is estimated at $22M; if demand turns out to be high, the firm could do nothing and realize a NPV of $46M, or could expand and realize a NPV of $50M. If the firm builds a large facility and demand is low, the NPV will be ($20M), whereas high demand will result in a NPV of $72M. a) Analyze and solve this problem using a decision…
2. If the projected or forecasted sales of Malinao Bakery for the month of Januaryis 2100 loaves of bread, beginning inventory 50 loaves and the selling price isP50 per loaves. How much are the projected sales in peso of Malinao Bakeryfor January?A. P100,000. C. P107,500.B. P100,500. D. P105,000.
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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…
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Franklin Company makes fine jewelry that it sells to department stores throughout the United States. Franklin is trying to decide which of the two bracelets to manufacture. Cost data pertaining to the two choices follow. Bracelet A Bracelet B Cost of materials per unit Cost of labor per unit Advertising cost per year Annual depreciation on existing equipment %24 30 37 43 43 8,800 6,500 7,700 5,900 Required a. Identify the fixed costs and determine the amount of fixed cost for each product. b. Identify the variable costs and determine the amount of variable cost per unit for each product. c. Identify the avoidable costs and determine the amount of avoidable cost for each product.