A small company manufactures three different electronic components for computers. Component A requires 2 hours offabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and componentC requires 2 hours of fabrication and 2 hours of assembly. The company has up to 1,200 labor-hours of fabrication timeand 1,050 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 company manufacture each week in order tomaximize 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 amathematical model in the form of a linear programming problem. A small company manufactures three different electronic components for computers. Component A requires 2 hours ofLet x₁, x₂, and x3 be the numbers of components A, B, and C, respectively, that get manufactured. Construct amathematical model in the form of a linear programming problem.Maximize P =subject toSSX₁, X2, X3 20Fabrication time restrictionAssembly time restriction

Component A Component B Component C Available Work hour Time required for fabrication (hour) 2 3…

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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Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of…
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-
Protective Research, Inc. received an order to produce a specially designed fence for preventing automobile accidents on the highways. The fence is manufactured in two sections, each requiring no more than 9 units of material A and no more than 6 units of material B. While each unit of material A weighs 4 kgs and B weighs 6 kgs, the final product must weigh exactly 48 kgs. Management figures profit in terms of input units, $240 per unit from material A and $160 from material B. What is the profitable mix.
A toy factory creates miniature steel train engines and box cars. The fabrication department has 3,679 minutes available per week and the assembly and finishing department has 3,099 minutes available per week. Manufacturing one miniature steel train engine requires 8 minutes of fabrication and 5 minutes of assembling and finishing. Manufacturing one miniature steel box car requires 4 minutes of fabrication and 5 minutes of assembling and finishing. The profit on each miniature steel train engine is $8.00 and the profit on each miniature steel box car is $7.25. How many steel train engines and steel box cars should be produced each week to obtain the maximum profit? Find the maximum weekly profit. (Use x for box car and y for train engine.) Maximize P subject to %3D < 3, 679 < 3, 099 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 toys…
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 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 2 hours 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 company manufacture 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 to X1, X₂, X3 20 The company should manufacture (Simplify your answers.) Fabrication time restriction Assembly time restriction…
A company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…
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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 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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