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A company produces two types of can openers: manual and electric. Each requires in its manufacture the use of two machines: A, and B. Each manual can opener requires the use of machine A for 2 hours, and machine B for 1 hour. An electric can opener requires 1 hour on A, and 2 hours on B. Furthermore, suppose the maximum numbers of hours available per month for the use of machines A, B are 90, 60 respectively. The profit on a manual can opener is $1.5, and on an electric can opener it is $2.5. If the company can sell all the can openers it can produce, how many of each type should it make in order to maximize the monthly profit? In order to solve this linear programming problem answer the following questions: Let us denote by • x = number of manual can openers • y = number of electric can openers i) For the objective function C(x, y) =ax +by we have • a= • b= ii) To maximize the profit, the company should produce manual can openers, and electric can openers. iii) The maximum profit is $

          A company produces two types of can openers: manual and electric. Each requires in its manufacture the use of two machines: A, and B. Each manual can opener requires the use of machine A for 2 hours, and machine B for 1 hour. An electric can opener requires 1 hour on A, and 2 hours on B. Furthermore, suppose the maximum numbers of hours available per month for the use of machines A, B are 90, 60 respectively. The profit on a manual can opener is $1.5, and on an electric can opener it is $2.5. If the company can sell all the can openers it can produce, how many of each type should it make in order to maximize the monthly profit?
In order to solve this linear programming problem answer the following questions:
Let us denote by
• x = number of manual can openers
• y = number of electric can openers
i) For the objective function C(x, y) =ax +by we have
• a=
• b=
ii) To maximize the profit, the company should produce manual can openers, and electric can openers.
iii) The maximum profit is $

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A company produces two types of can openers: manual and electric. Each requires in its manufacture the use of two machines: A, and B. Each manual can opener requires the use of machine A for 2 hours, and machine B for 1 hour. An electric can opener requires 1 hour on A, and 2 hours on B. Furthermore, suppose the maximum numbers of hours available per month for the use of machines A, B are 90, 60 respectively. The profit on a manual can opener is 1.5, and on an electric can opener it is2.5. If the company can sell all the can openers it can produce, how many of each type should it make in order to maximize the monthly profit?
In order to solve this linear programming problem answer the following questions:
Let us denote by
• x = number of manual can openers
• y = number of electric can openers
i) For the objective function C(x, y) =ax +by we have
• a=
• b=
ii) To maximize the profit, the company should produce manual can openers, and electric can openers.
iii) The maximum profit is

Added by Mark R.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Keondre Parker

11/01/2022

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5y \), where \( x \) represents the number of manual can openers and \( y \) represents the number of electric can openers. Show more…

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A company produces two types of can openers: manual and electric. Each requires in its manufacture the use of two machines: A and B. Each manual can opener requires the use of machine A for 2 hours and machine B for 1 hour. An electric can opener requires 1 hour on machine A and 2 hours on machine B. Furthermore, suppose the maximum numbers of hours available per month for the use of machines A and B are 90 and 60 respectively. The profit on a manual can opener is $1.5, and on an electric opener, it is $2.5. If the company can sell all the can openers it can produce, how many of each type should it make in order to maximize the monthly profit? In order to solve this linear programming problem, answer the following questions: Let us denote by * x = number of manual can openers * y = number of electric can openers i) For the objective function C(x, y) = ax + by, we have * a= * b= ii) To maximize the profit, the company should produce manual can openers, and electric can openers. iii) The maximum profit is $

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Transcript

00:01 All right, so we want to produce two types of can openers.

00:04 We have manual and the electric.

00:10 Manual and then we have the electric.

00:14 So we know that we use two different types of machines, machines a and b, to produce these two.

00:21 So for the manual can opener, it requires two hours machine a and one hour machine b.

00:31 So for the electric, for the machine a, to produce it, it takes, two hours here and then machine b takes one hour here and then for the electric it takes one hour on a machine a and two hours on b and we know that the maximum number of hours available per month for using machines are 90 and 60 so the total hours are going to be 90 and 60 so we want to know so so we can make a profit on.

01:36 So our profit would be $1 .50 for selling the number of can openers, our manual, plus 2 .5 for the electric.

02:13 So we want to try to sell all of those.

02:16 So we want to try to maximize this.

02:18 So we know our objective function, which is c of x, y.

02:27 It would be a x plus b y so in that case solving this out we're going to have the equation that's 2x plus y even 90 and x plus 2y equal to 60 so let's get rid of the x let's multiply the denominator by negative 2.

03:11 I'm not the denominator the bottom equation by negative 2.

03:20 They have negative 2 x minus 4x, i mean 4 y, it should be negative 120...

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