Problem 1Consider the following production problem. A furniture company builds tables and chairs using only woodand nails. Each table requires 4 planks of wood and 2 boxes of nails. Each chair requires 1 plank of woodand 2 boxes of nails. The company currently has 2000 planks of wood and 1200 boxes of nails. Each tableyou build can be sold for $100 and each chair can be sold for $40.a) Formulate an LP that will solve this problem. (Assume that you can build fractional tables and chairs.)b) Now formulate the dual for this problem.c) Using Excel, solve the dual LP. Write up your solution. Also print out and attach your Answer Report.

Concept Used There is always a corresponding Linear Programming Problem (LPP) associated with every…

Answered: Problem 1 Consider the following…

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 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.
4. A company has a total of 500 light bulbs that are 100 watts each. The cost for electricity is 0.18 cents per kilowatt-hour. If all the bulbs are on 24 hours a day for 30 days, how much will the cost be?
Change this LP problem (e.g., money, time, or number of batches), so that it has at least two whole number solutions: A bakery makes both chocolate cakes and almond cookies. Each batch of cakes requires 2hours in the oven and 3hours into decorating room. Each batch of cookies requires 1hour and 30 minutes in the oven and 30 minutes into the decorating room. The oven is available no more than 15hours per day, and the decorating room can be used no more than 13hours per day. The Daily profit from production of one batch of cakes is $50 and one batch of cookies is $15. How Many batches of cakes and cookies should be produced daily in order to maximize bakery's 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 $1.00)?$
A patient takes vitamin pills. Each day he must have at least 300IU of vitamin A, 3 mg of vitamin B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B1, and 40 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 50¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy nothing of pill 1 and nothing of pill 2. The minimum cost is $ nothing. (Simplify your answers. Type integers or decimals.)
A tent manufacture produces regular and expedition tents at three branches. Per hour of operation, the Harrogate branch produces 20 regular tents and 10 expedition tents. The Skipton branch produces 0 regular tents and 20 expedition tents, and the York branc h produces 80 regular tents and 20 expedition tents. In order to meet the demand, the company needs to produce exactly 240 regular tents and 100 expedition tents each day. How many hours per day should each branch operate in order to produce the required amounts of tent? Solve using Gauss-Jordan elimination method.
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 2000 units of product A, up to 3000 units of product B, and up to 5000 units of prod-uct C. Each unit of product C uses two units of A and three units of B and incurs $7 in processing costs. Prod-ucts A and B are produced from either raw material 1 or raw material 2. It costs $9 to purchase and process one unit of raw material 1. Each processed unit of raw mate-rial 1 yields two units of A and four units of B. It costs $5 to purchase and process a unit of raw material 2.Each processed unit of raw material 2 yields one unit ofA and three units of B. The unit prices for the products are: A, $10; B, $9; and C, $32. The quality levels ofeach product are: A, 7; B, 9; and C, 6. The average quality level of the units sold must be at least 8. Deter-mine how to maximize Bexter’s profit.

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