Prime Paints manufactures two types of paints, one for interior painting and theother for exterior painting. Both types require the use of two raw materials - M1and M2, so that the maximum daily availabilities of these materials are 24 tonsand 6 tons, respectively. It is known that 1 ton of the interior type of paintrequires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exteriortype of paint requires 6 tons of M1 and 1 ton of M2. It has been established thatthe daily demand for interior paint cannot exceed that for the exterior paint bymore 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 andexterior paints to maximize the total daily profit given that the profit per ton ofthe interior paint is 4 thousand dollars and the profit per ton of the exterior paintis 5 thousand dollars.Suppose x represents the number of tons produced daily of interior paints and yrepresents the number of tons produced daily of exterior paints. Which of thefollowing describes the constraint pertaining to the market limit of theseproducts?y – x <1x - y<1Y< 2x < 2

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Answered: Prime Paints manufactures two types of…

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 brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the boors, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost por unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of reqular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery noeds at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? 30 units of regular beer and 20 units of light beer should be made, for a minimum total cost of $ 2160000 (Type integers or decimals.) (b) Suppose the minimum revenue is increased to $9,400,000. Use shadow costs to calculate the total…
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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. Suppose x represents the number of tons produced daily of interior paints and y represents…
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.
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