Consider the following optimization problem:Prime Paints manufactures two types of paints, one for interior painting and the otherfor exterior painting. Both types require the use of two raw materials - M1 and M2, sothat the maximum daily availabilities of these materials are 24 tons and 6 tons,respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tonsof M1 and 1 ton of M2. It has been established that the daily demand for interiorpaint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximumdaily demand for interior paint is 2 tons. The company wants to determine theoptimum product mix of interior and exterior paints to maximize the total daily profitgiven that the profit per ton of the interior paint is 4 thousand dollars and the profitper ton of the exterior paint is 5 thousand dollars.Which of the following is the aim of the company?Minimize costMinimize timeMaximize revenueMaximize profit

We will construct a linear programming problem according to the given conditions. Let x ton and y…

Answered: Consider the following optimization…

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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need comprehensive and correct answers.This question is about optimization.
Two supply depots (S1 and S2) can serve the demand for three demand centers (D1, D2 and D3). The cost to transport one unit of supply from supply depot to demand center is shown on the table below. Supply depot 1 has 1,200 available units, while depot 2 has 2,000. The demand centers have 1,200 units, 1,300 units and 700 units for D1, D2 and D3, respectively. In the optimal allocation, how many units should supply depot 1 allocate to demand center 1? Use northwest corner method in determining the initial feasible solution. For determining the optimal solution, you can choose either of the two methods (stepping stone and MODI).
In "Blingblong Takes the World", a famous online role-playing game, the titular character's total damage is computed by taking the product of the critical rate x and critical damage y under the constraint x + % maximum damage to an opponent if c = 100%. = c. Find the critical rate and critical damage needed to inflict the
A local electricity company produces and distributes electricity to residential customers. The firm is a monopoly and it is regulated such that p = MC. The firm faces the following demand function: p = 800 – 2g and its total cost function is: C = 22500 + 200g + q². a) Find the deadweight loss that would result if this company was allowed to operate as a profit maximizing firm, compared to the situation under regulation. b) Calculate the Lerner index of Monopoly Power at the profit maximizing point.
A small paint company specializes in two types of exterior paint: latex and enamel paint. It requires 10 labor-hours per 100 liters of latex paint and 15 labor-hours per 100 liters of enamel paint. It is assumed that the company works only 40 hours per week, does not hire additional labor, and does not engage in overtime work. From 1 liter of latex paint, a profit of 5 units is obtained, while from 1 liter of enamel paint, a profit of 10 units is obtained. The owner of the company prioritizes the objectives in the following order: Avoiding overtime work Maintaining a weekly profit of at least 1000 units Producing a minimum of 700 liters of enamel paint each week to meet the demand of an existing customer Formulate the goal programming model for the company.
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day. 0 Graph the system of inequalities, remember to include x >0 and y > 0 in your graph to get full credit. You will need to include four lines. 25 24 VI
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars.
A company is dedicated to the production of different vegetable-flavored milks. Currently the company produces two types of milk: almond and coconut, which it sells at $ 5,000 and $ 2,000 / liter respectively. Milk production is subject to the use of machine hours in the production plant and of water as a fundamental resource. It takes 1 machine-hour and 2 liters of water to produce 1 liter of almond milk, while it takes 3 machine-hours and 1 liter of water to produce 1 liter of coconut milk. The company currently has 100 machine-hours and 50 liters of water to make the milk, and it is also required to make at least 30 liters of milk in total. 1. Set up the linear programming model in standard format.2. Determine all the basic solutions to the problem. Identify which ones are feasible and which ones are not. Analyze what happens graphically.3. Determine an initial feasible basic solution using phase I. In each iteration, write the resulting model in dictionary format and analyze what…

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