5. A manufacturing company makes two models A and B of a product. Each piece of Model Arequires 12 labor hours for fabricating and 1 labor hour for finishing. Each piece of Model Brequires 6 labor hours for fabricating and 3 labor hours for finishing. For fabricating andfinishing, the maximum labor hours available are 150 and 60 respectively. The company makesa profit of $10000 on each piece of model A and $9000 on each piece of Model B. How manypieces of Model A and Model B should be manufactured per week to realize a maximum profit?What is the maximum profit per week?

Given- A manufacturing company makes two models A and B of a product. Each piece of the Model A…

Answered: 5. A manufacturing company makes two…

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 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 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.)
It takes 12 units of carbohydrates and 6 units of protein to satisfy Jacob's minimum weekly requirements. The meat contains 2 units of carbohydrates and 2 units of protein per pound. The cheese contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.40 per pound and the cheese costs $4.50 per pound. How many pounds of each are needed to fulfill the minimum requirements at minimum cost? What is Jacob's minimum cost? He should buy pound(s) of meat and pound(s) of cheese. (Round your answer to the nearest tenth.) The minimum cost is $. (Round to the nearest cent as needed.) ...
please see the attached question. thanks for your help
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
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.
.
Suppose that a small company produces two different models of kayaks. A larger model and smaller model. The larger model requires 2 hours of manufacturing, 2 hours for assembly and 3 hours for packaging. The smaller model requires 2 hours for manufacturing, 1 hour for assembly and 2 hours for packaging. Each week the company has 120 hours available for manufacturing, 80 hours available for assembly and 132 hours available for packaging. If the company makes a profit of $75 for each of the larger model manufactured and profit of $60 for each smaller model manufactured, how many of each model should the company produce in order to maximize profit ?
Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of Super- Fit takes 12 minutes to cut and 30 minutes to sew and finish. Each pair of Super-Hug takes 12 minutes to cut and 40 minutes to sew and finish. The plant has enough workers to provide at most 12,599 minutes per day for cutting and at most 37,999 minutes per day for sewing and finishing. The profit on each pair of Super-Fit is $6.00 and the profit on each pair of Super-Hug is $7.00. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. (Use x for Super-Fit and y for Super-Hug.) Maximize P = < 12,599 ≤37,999 Maximum profit is $ subject to 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 jeans to…

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