LINEAR PROGRAMMING PROBLEMS1. A laboratory wishes to purchase two different types of feed, A andB, for its animals. Type A feed has 2 units of carbohydrates perpound and 4 units of protein per pound. Type B feed has 8 units ofcarbohydrates per pound and 2 units of protein per pound. Feed Acosts 1.40 per pound and feed B costs 1.60 per pound. If at least 80units of carbohydrates and 132 units of protein are required, howmany pounds of each feed are required to minimize the cost? Whatis the minimal cost?(32 units of feed A and 2 units of feed B; Minimum Cost: $48)2. Evergreen Company produces two types of printers, Inkjet andLaserjet. The company can make at most 120 printers per day andhas 400 labor-hours available per day. It takes 2 hours to make theInkjet and 6 hours to make the Laserjet. If the profit on the Inkjetis $80 and profit on the Laserjet is $120, find how many of eachprinter to yield the maximum profit and the maximum profit.(80 Inkjet, 40 Laserjet; Max. Profit $11,200)=3. A company manufactures two types of computer chips, one thatruns at 2.0 GHz and the other that runs at 2.8 GHz. The companycan make a maximum of 50 fast chips and 100 slow chips per day.It takes 6 hours to make a fast chip and 3 hours to make a slowchip, and the employees can provide up to 360 hours of labor perday. The company makes a profit of $20 on each fast chip and $27on each slow chip. How many of each should be made to maximizeprofit? List the maximum profit.(10 fast chips and 100 slow chips)4. A laboratory wishes to purchase two different types of feed, Aand B, for its animals. Type A feed has 2 units of carbohydratesper pound and 4 units of protein per pound. Type B feed has 6units of carbohydrates per pound and 2 units of protein perpound. Feed A costs 1.40 per pound and feed B costs 1.60 perpound. If at least 30 units of carbohydrates and 40 units ofprotein are required, how many pounds of each feed arerequired to minimize the cost? What is the minimal cost?(9 units of A and 2 units of B; Minimum Cost: $15.80)

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Answered: LINEAR PROGRAMMING PROBLEMS 1. A…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: 2 = 40p.5 p0.5 Chemical P costs $200 a unit and chemical R costs $400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $32,000. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units
11. A small country exports soybeans and flowers. Soybeans require 8 workers per acre, flowers require 12 workers per acre and 100,000 workers are available. Government contracts require that there be at least 3 times as many acres of soybeans as flowers planted. It costs $250 per acre to plant soybeans and $300 per acre to plant flowers, and there is a budget of $3 million. If the profit from soybeans is $1,800 per acre and the profit from flowers is $2,000 per acre, how many acres of each crop should be planted to maximize profit? Then find the maximum profit.
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1, and each Type B souvenir will result in a profit of $1.20. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 3 hours available on Machine I and 5 hours available on Machine II. (a) The optimal solution holds if the contribution to the profit of a Type B souvenir lies between $ 48 X and $ 96 X. (Enter your answers from smallest to largest.) (b) Find the contribution to the profit of a Type A souvenir (with the contribution to the profit of a Type B souvenir held at $1.20), given that the optimal profit of the company will be $196.80. $2 (c) What will be the optimal profit of the company if the contribution to the profit of a Type B souvenir is $1.50 (with the contribution to the profit of a Type A souvenir held at $1.00)? $168
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1, and each Type B souvenir will result in a profit of $1.20. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 3 hours available on Machine I and 5 hours available on Machine II. (a) The optimal solution holds if the contribution to the profit of a Type B souvenir lies between $ and $ . (Enter your answers from smallest to largest.)(b) Find the contribution to the profit of a Type A souvenir (with the contribution to the profit of a Type B souvenir held at $1.20), given that the optimal profit of the company will be $208.80.$ (c) What will be the optimal profit of the company if the contribution to the profit of a Type B souvenir is $2.00 (with the contribution to the profit of a Type A souvenir held at $1.00)?$
1. Mary has been placed on a strict diet. She monitors her food very carefully. One day at lunch, she plans to have tuna fish sandwiches and tomato soup. The nutrients per serving are found in the table below: Fat (g) Sodium (mg) Protein Sandwich 10 200 20 Soup 4 400 10 Mary can have no more than 34 grams of fat and 1000 mg of sodium. How many servings of soup and sandwich can she have for lunch to maximize her protein intake? a) Define the variables: b) What are the constraint inequalities? Inequality concerning sodium: Inequality concerning fat: c) What is the objective function?
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A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine Il per month are 7,760 and 10,080. The time requirements and profit per unit for each product are listed below. ABC Machine I 7 9 10 Machine II 8 10 16 $12 $16 $22 Profit How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced. Maximize P = subject to: <7,760 s 10,080 Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimal places. The maximum profit is $ when the company produces: units of product A units of product B units of product c

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