GA company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires2 hours to make, and the cordless model requires 4 hours. The company has only 800 work hours to use in manufacturingeach day, and the packaging department can package only 300 trimmers per day. If the company profits are $36.50 for thecord-type model and $73.00 for the cordless model, how many of each type should the company produce per day tomaximize profits?Scenario #1 (with the smaller number of cord-type trimmers):corded modelscordless modelsScenario #2 (with the larger number of cord-type trimmers):corded modelscordless modelsNeed Help?Read ItMaster It

This question can be solved using the concept of linear programming.

Answered: A company manufactures two types of…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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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, two 2 ✕ 4's, and four sheets of plywood. The carpenter has 55 boxes of screws, 70 2 ✕ 4's, and 115 sheets of plywood on hand. In order to maximize their profit using these materials on hand, the carpenter has determined that they must build 10 shelves and 20 tables. How many of each of the materials (boxes of screws, 2 ✕ 4's, and sheets of plywood) are leftover, when the carpenter builds 10 shelves and 20 tables? The carpenter has _ boxes of screws, _ 2 ✕ 4's, and _ sheets of plywood leftover.
The research department at a manufacturing company has developed a new process that it believes will result in an improved product. Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market it, sales should increase by $70,000. If it is not better and they replace the old product with the new product on the market, they will lose $25,000 to competitors. If they decide not to market the new product, they will lose a total of $60,000 if it is better and just research costs of $20,000 if it is not. Complete parts (a) and (b) below. (a) Prepare a payoff matrix. □ (Type an integer or decimal for each matrix element. Do not include the $ symbol in your answer.)
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 $1.00)?$
McJester's Burger Hut plans to expand by opening several new restaurants. The chain operates two types of restaurants: drive-through and full-service. A drive-through restaurant costs $111,000 to construct, requires 7 employees, and has an expected annual revenue of $205,000. A full-service restaurant costs $184,000 to construct, requires 17 employees, and has an expected annual revenue of $565,000. McJester's has $3,250,000 in capital available for expansion. Labor contracts require that they higher no more than 325 employees. Licensing restrictions require that they open no more than 25 new restaurants. Let x be the number of drive-through restaurants and let y be the number of full-service restaurants in this expansion. Let R be the expected annual revenue in dollars resulting from the expansion. McJester's wants to maximize the expected revenue. Set up the linear programming problem. Answer the following questions about this linear programming problem. The question is attached…
The E-JEM Company produces two types of laptop computer bags. The regular version requires $32 in capital, 4 hours of labor, and sells for $41. The deluxe version requires $38 in capital, 6 hours of labor, and sells for $52. How many of each type of bag should the company produce in order to maximize their revenue if they have $2100 and 300 labor hours available? ..... The company should make regular laptop bags and deluxe bags to maximize revenue.
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200, and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. What are the binding constraints of the feasible region of the optimal solution? Constraint 2 only Constraint 1 only…
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 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.
Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 4 hours of work from Carlo and 4 hours from Anita. Each toy requires 2 hours of work from Carlo and 4 hours from Anita. Carlo cannot work more than 16 hours per week and Anita cannot work more than 20 hours per week. If each mailbox sells for $9 and each toy sells for $13, then how many of each should they make to maximize their revenue? What is their maximum revenue? ---- Carlo and Anita should make mailboxes and toys. Their maximum revenue is $
McJester's Burger Hut plans to expand by opening several new restaurants. The chain operates two types of restaurants: drive-through and full-service. A drive-through restaurant costs $111,000 to construct, requires 7 employees, and has an expected annual revenue of $205,000. A full-service restaurant costs $184,000 to construct, requires 17 employees, and has an expected annual revenue of $565,000. McJester's has $3,250,000 in capital available for expansion. Labor contracts require that they higher no more than 325 employees. Licensing restrictions require that they open no more than 25 new restaurants. Let x be the number of drive-through restaurants and let y be the number of full-service restaurants in this expansion. Let R be the expected annual revenue in dollars resulting from the expansion. McJester's wants to maximize the expected revenue. Set up the linear programming problem. Answer the following questions about this linear programming problem. The question is attached…

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