A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2hours of assembly. The company has up to 900 labor-hours of fabrication time and 700 labor-hours of assembly time available per week. The profit on each component, A, B, and C, is $7, $8, and $10, respectively. How many components of each type should the companymanufacture each week in order to maximize its profit (assuming that all components manufactured can be sold)? What is the maximum profit?Let x₁, x2, and x3 be the numbers of components A, B, and C, respectively, that get manufactured. Construct a mathematical model in the form of a linear programming problem.Maximize P=[subject toX1, X₂, X3 20The company should manufacture(Simplify your answers.)Fabrication time restrictionAssembly time restrictioncomponent As,component Bs, andCcomponent Cs to maximize their profit at $

A small company manufactures three different electronic components for computers. Component A…

Answered: A small company manufactures three…

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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Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of Super-Fit takes 14 minutes to cut and 15 minutes to sew and finish. Each pair of Super-Hug takes 14 minutes to cut and 35 minutes to sew and finish. The plant has enough workers to provide at most 13,999 minutes per day for cutting and at most 25,999 minutes per day for sewing and finishing. The profit on each pair of Super-Fit is $4.00 and the profit on each pair of Super-Hug is $5.00. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. (Use for Super-Fit and y for Super-Hug.) Maximize P = 4.00x + 5.00y subject to 14x + 14y 13, 999 15x + 35y 25, 999 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round jeans to 1 decimal place and profit to 2 decimal places. Number of Super-Fit…
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $0.80, and each Type B souvenir will result in a profit of $1.00. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 2 hours available on Machine I and 5 hours available on Machine II. (a) For a meaningful solution, the time available on Machine II must lie between and min. (Enter your answers from smallest to largest.)(b) If the time available on Machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing Type A souvenirs and Type B souvenirs, where ≤ k ≤ .(c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.)$
A company makes pancake mix and cake mix. Each pound of pancake mix uses 0.6 lb of flour and 0.1 lb of shortening. Each pound of cake mix uses 0.4 lb of flour, 0.1 lb of shortening, and 0.4 lb of sugar. Suppliers can deliver at most 6,000 lb of flour, at least 500 lb of shortening, and at most 1,200 lb of sugar. If the profit per pound is $0.45 for pancake mix and $0.35 for cake mix, how many pounds of each mix should be made to earn maximum profit? pancake mix 2000 Xlb lb cake mix 3000 What is the maximum profit (in $)? $3450 X
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 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 $ THER 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 $3.00 (with the contribution to the profit of a Type A souvenir held at $1.00)? $
2. A small company manufactures 3 different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 1 hr of fabrication and 2 hours of assembly, and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 1000 labor-hours of fabrication time and 800 labor-hours of assembly time available per week. The profit on each component A, B, and C is $7, 9, and 10 respectively. How many components of each type should the company manufacture each week in order to maximize its profit? What is the maximum profit?
A company manufactures paring knives and pocket knives. Each paring knife requires 3 labor-hours, 7 units of steel, and 4 units of wood. Each pocket knife requires 6 labor-hours, 5 units of steel, and 3 units of wood. The profit on each paring knife is $3, and the profit on each pocket knife is $5. Each day the company has available 102 labor-hours, 157 units of steel, and 123 units of wood. Suppose that the number of labor-hours that are available each day is increased by h. For what values of h will a change of h labor-hours not change the shadow price of labor? The shadow price of labor will not change for shs. (Simplify your answers.)
erth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $15,000/day to operate, and it yields 65 oz of gold and 2900 oz of silver each day. The Horseshoe Mine costs $15,500/day to operate, and it yields 70 oz of gold and 1300 oz of silver each day. Company management has set a target of at least 540 oz of gold and 16,800 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost? Saddle- Days Horseshoe- Days Minimum Cost-
A game company is developing two new games, a board game, and a mechanical game. Each board game requires 1/2 hr to manufacture, 1/2 hr to assemble, and 1/2 to inspect and package. In given week there are 40 hours available for manufacturing, 32 hours available for assembly, and 18 hours available for inspection and packaging. Suppose the profit on each game is $10 and the profit on each mechanical game is $15. How many of each game should be produced each week for maximum profit?
Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize P = 1.75x + 1.25y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize P = 2x + 1.5y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
A manufacturer produces two models of toy airplanes. It takes the manufacturer 32 minutes to assemble model A and 8 minutes to package it. It takes the manufacturer 20 minutes to assemble model B and 10 minutes to package it. In a given week, the total available time for assembling is 3200 minutes, and the total available time for packaging is 960 minutes. Model A earns a profit of $10 for each unit sold and model B earns a profit of $8 for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week? Note that the ALEKS graphing calculator can be used to make computations easier. k trol Model A: unit(s) Model B: unit(s) Continue 1 Q A 2 option X NO 2 Z W S 5 # 3 ME P X E H command $ 4 D 9 R C % 5 F T A V 6 FO G Y 8 7 B Submit A © 2023 McGraw HRLLC Al Rights Reserved forms of Use | Plicy Center the # WY 8 U Deft FN J N 3 9 K M O < P 1 g
A carpenter builds bookshelves and tables for a living. Each bookshelf takes one box of screws, two 2 ✕ 4's, and three sheets of plywood to make. Each table takes two boxes of screws, four 2 ✕ 4's, and four sheets of plywood. The carpenter has 80 boxes of screws, 145 2 ✕ 4's, and 170 sheets of plywood on hand. In order to maximize their profit using these materials on hand, the carpenter has determined that they must build 12 shelves and 29 tables. How many of each of the materials (boxes of screws, 2 ✕ 4's, and sheets of plywood) are leftover, when the carpenter builds 12 shelves and 29 tables? The carpenter has boxes of screws, 2 ✕ 4's, and sheets of plywood leftover.

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